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The city of Hawija has a likely current population of around 70,000. Though it is, in theory, under siege by Peshmerga fighters to the north and east, and Iraqi government forces and the Popular Mobilisation Front (PMF) to the south and west, the Islamic State group has been able to move in and out of it quite freely.

The battle for Hawija will not be as significant as the gruelling nine-month fight for Mosul, but it lies close to an area that has been an ungovernable haven for insurgent groups for many years - and perhaps indicates what a future IS, short of governable territory, at least in Iraq, might look like.

Hawija serves IS well with its proximity to the Hamrin mountains to its south east. The modest mountain range has been an insurgent hub since 2003. Before that, it was part of the vast smuggling networks run by local tribes and utilised by Saddam Hussein to get round sanctions. Even when the US coalition had hundreds of thousands of troops in the country, it was still something of a no-mans-land.

While all proper roads in and out of "the Hawija pocket" are controlled by Iraqi troops or Kurdish Peshmerga fighters, routes through the Hamrin mountains act as natural thoroughfares that connect the area with both Diyala and Salahuddin provinces - two parts of Iraq that have seen a significant recent uptake in IS activity. 

IS appears to have anticipated their withdrawal from much of their territory, and have long prepared to hide out here in the mountains for a return to insurgency

Analysts Michael Knights and Alex Mello as referring to rural Diyala as a "terrorist haven". Recent IS propaganda from the provinces can see the jihadists openly moving through the Hamrin mountains in almost brazen fashion.

Closing down these routes is also made harder by the fact that they are also used as relatively safe passage for innocent displaced locals fleeing the area.

IS appears to have anticipated their withdrawal from much of their territory, and have long prepared to hide out here in the mountains for a return to insurgency. As early as last December, a spokesperson for the Badr Organisation claimed the militia had destroyed an IS hideout in the Hamrin mountains including "a warehouse containing food materials".

The routes out of the Hawija pocket were obscure and treacherous even before the arrival of IS, with even many locals not knowing the exact safe paths through the perilous terrain. Recent months have seen IS heavily mine these tracks, particularly those that lead into the mountains. Of course, the group has left certain corridors mine-free for their own fighters to use, and these have been exploited by smugglers operating out of the small village of Al-Kahwa, around 10 kilometres southeast of Hawija. 

Locals sources claim these smugglers charge between $150 to $200 to reveal the safe routes into the mountains - and that dozens of people, either unable or unwilling to pay the smugglers, have been killed attempting to navigate themselves through the minefields.

Most recently, on August 16, three civilians were killed and seven injured attempting to flee to Al-Alam via one of the mountain routes. The mining of the mountain paths is not only treacherous for civilians trying to flee, but will severely hamper any efforts by the security forces to pursue insurgents into the mountain range.

The geographical protection offered by the pocket has also allowed IS to conduct frequent surprise attacks, as well as raids on nearby bases and weapons dumps - particularly those controlled by the Peshmerga. A recent IS video showed long-range sniper attacks against the Kurdish forces, and Peshmerga commanders have claimed such shootings happens daily. It was operating from the Hawija pocket that IS was able to take back the village of Imam Gharbi, near Mosul, for several weeks in July.

Hawija is also home to what remains of IS' oil industry in Iraq. Iraq Oil Report that militants were still able to tap into oil in the Hamrin area, and refine it at the now disused Iraqi Army Base 46, and at other local makeshift refineries.

The Hawija pocket is not under the direct control of one IS "province", or wilayat - the area covers the western part of Wilayat Kirkuk and parts of eastern Wilayat Dijlah. But while IS here is still producing branded propaganda from two separate provincial franchises, the two wilayats appear to have been merged on an administrative level to some extent.

A man known as Abu Haytham currently serves as the wali, or administrator, of both Kirkuk and Dijlah. His real name is Qusay Hassan Wali Al-Bayati, but little is known about him. Security sources say he hails from Al-Tooz district in Salahuddin province. He last appeared in public in a video released in April 2015, addressing fighters before a raid on Peshmerga positions.

The PMF, an umbrella group of mostly Shia militias fighting IS, erroneously claimed he had been killed in a coalition airstrike this year. He also hit headlines with (seemingly unfounded) reports suggesting that he had assumed the title of caliph following Abu Bakr Al-Baghdad's rumoured death. A mugshot of him suggests he spent time in either Iraqi, or more likely, American prisons.

On a provincial level, Abu Haytham is supported by two deputies; Abu Sa'ad Al-Bayati and Abu Abd Aleem. The town of Hawija itself is headed by Ghraith Ibrahim Murad from nearby Sheikh Hamad. Murad is a second generation jihadist; his father, Diyab, serves as a lower level IS commander also within the Hawija pocket.

Ghraith has a long history of militancy dating back to at least 2009; back then he served as an "assassin" for the Islamic State of Iraq, the predecessor to IS, in Mosul.

He was eventually captured and imprisoned in Tikrit - until September 2012, when he managed to escape. He was recaptured in 2013, but found himself free once more after being broken out of prison during IS' "Breaking of the Walls" campaign. He then became active in the fighting against the Iraqi military in Mosul, until he was reportedly injured in a coalition airstrike in December 2016. It was after this point he was redeployed to Wilayat Kirkuk and later became "Emir of Hawija".

Within Hawija, IS' main fighting force is the Saladin Battalion - primarily made up of Kurdish fighters, not Arabs. Abu Ziyad Al-Kurdi, the IS "emir" of the nearby town of Al-Rashad, is also a Kurd from the city of Chamchamal, around 30 kilometres west of Kirkuk.

Kurds have played a relatively prominent role in some of the propaganda produced in this area in the past few years, with one video, released in February 2015 and featuring IS prisoners paraded in cages, recorded in Kurdish and subtitled in Arabic. These wilayats were the natural destinations for Iraqi Kurds looking to join the group. IS were aware of that, and appear to have targeted their recruitment media accordingly.

Security sources estimate that Hawija may be home to up to 1,000 IS fighters, though even if that number is an over-estimate on the scale of what was seen in Tal Afar, what IS lack in numbers here, they make up for in local knowledge.

The militia has, however, been hit by internal clashes - particularly in recent days.

Since the fall of Mosul, violent clashes have reportedly broken out between foreign and local members, with locals attempting to ostracise and push out foreign fighters from decision-making positions. Villagers have openly taken to Facebook that the disappearance of a local man, Atieh Salman, was a catalyst for the rift developing. Several IS fighters are understood to have been killed in the dispute. But the one foreigner who does not appear to have fallen foul of this falling-out is "the emir of Al-Zab", a Chechen fighter named Abu Bakr Al-Shishani.

With such internal feuding, it's not just the advancing troops that are putting the Islamic State group under pressure in Hawija.