ISIS’s territorial gains in Syria and Iraq are impressive. However, the group has its work cut out for it.

First, ISIS may face internal tensions. The nature of the relationship between the group and Iraqi Baathists has been variously reported. While the two have an obvious operational incentive to collaborate, if the former Baathist elements retain their original ideological platform, it is likely incompatible with ISIS’s radical preferences. Should ISIS determine it is content with its territorial holdings, any partnership could face tensions in the absence of a common enemy in Maliki’s sectarian rule.

Second, the Kurds. ISIS appears to have largely avoided direct confrontation with Kurdish forces. But the Kurds appear far from assuming ISIS is an ally, or that the group does not have designs on territory the Kurds themselves claim. If and when ISIS and Kurdish ambitions clash, the peshmerga are likely to put up a fight.

Third, ISIS may be able to take territory, but it now faces the challenge of ruling it. The group has a track record over the last year of ruling in Syrian cities like Raqqa. In Syria, ISIS rebels provided public services, and tried to moderate their implementation of sharia law so as to avoid civilian resistance. But gradually the group reverted to its own ideological platform—an Islamic interpretation not in line with that of the Syrian civilians under their rule. In order to tamp down public dissent and quell resistance, the rebels have become notoriously brutal—showcasing their brutality publicly and electronically. In Iraq, at least some civilians have welcomed ISIS’s arrival and the Iraqi military’s departure. But preferring ISIS to Maliki isn’t necessarily saying a lot.

The US also sought to control areas ISIS now claims in Iraq, and America’s limited success was hard-won. ISIS’s acceptability as a ruler remains to be seen (the group has just published its first set of rules for those newly under its control). As time wears on, any distance between ISIS’s political and ideological platform and those of its new residents will become clearer. If, as in Syria, this gap proves to be wide, we may expect similarly brutal rule by ISIS in Iraq.

If so, the international community will need to weigh the suffering of those under ISIS control against the likely costs and success of intervening to improve the situation.

Unless they moderate their platform, there are few ways to encourage ISIS to adopt less coercive rule. Interdicting support from abroad can strain the group in a variety of ways, but access to oil wealth (and now, cash) will dampen the effects of any interdiction, and even a weakened ISIS is likely to abuse civilians.

But beyond the first blush of victory, governance is a difficult and costly undertaking. Reports note ISIS’s extensive and coercive reach into civilians’ lives in Syrian cities it has controlled since last year. But this apparatus eats up resources. Even if ISIS uses public brutality to quash resistance and retain control, it will have to task personnel to do this—personnel that cannot then be used to pursue additional territory, or protect themselves against government troops or other rival factions.

Unfortunately for those who live under it, brutality can be a sustainable means of retaining control—for rebels like ISIS, as well as for states. ISIS may manage to keep the territory it has captured, but it will have to work for it—as Ghengis Khan noted “Conquering the world on horseback is easy; it is dismounting and governing that is hard.”