In the Syrian city of Raqqah on the banks of the Euphrates River, Islamic State militants are busy building a capital fit for their followers.

Human rights observers say they have stoned women to death for adultery, while residents report that religious textbooks have been imported for schools and the market flooded with black cloaks for girls as young as 6 years old. Even as it wages war on multiple fronts, the group has had time to focus on the details, recruit thousands into its forces and celebrate victories by parading the heads of its enemies.

It’s a reflection of how entrenched the group has become in Syria and how difficult it will be to uproot it from the country where it was able to assemble and train enough forces to push into Iraq in June. U.S. airstrikes alone won’t do it and the international community doesn’t have any other options to fall back on, Kamran Bokhari, vice-president for the Middle East at Texas-based consulting firm Stratfor, said from Toronto.

“Who’s the other force that’s going to fight the Islamic State on the ground?” said Bokhari. “Its presence in Iraq is based on its strategic depth in Syria and to truly eliminate the threat from Iraq you have to weaken it in Syria.”

U.S. President Barack Obama ordered airstrikes this month against the Islamist militants in Iraq, though he hasn’t approved action against the group inside Syria.

Syrian President Bashar al-Assad’s government, which has said that its three-year civil war has been against foreign-backed terrorists rather than freedom-seeking protesters, offered to cooperate in the fight against the extremists.

Foreign Minister Walid al-Muallem said on Aug. 25 any counter-terrorism effort must be done in coordination with the Syrian government, a demand that White House press secretary Josh Earnest has dismissed.

French President Francois Hollande said Assad can’t be an ally in the battle against terror. Assad is an “objective ally” of the Islamic State, Hollande told French ambassadors in Paris.

The U.S. is aiming to tackle the Islamic State without helping the Assad regime, though that may prove difficult, according to Michael Desch, professor of political science at the University of Notre Dame.

“This is a circle that can’t be squared,” Desch said by e-mail. “In both Saddam Hussein’s Iraq and now Assad’s Syria we tried to overthrow brutal dictators only to find that their replacements were even worse.” Islamic State “is far more of a threat than Assad and if attacking the former bolsters the latter, so be it,” he said.

The Islamic State, which evolved from the al-Qaeda in Iraq, appeared in Syria two years after the anti-Assad uprising began, emerging in April 2013 following its break from the al-Qaeda-affiliated al-Nusra Front.

Initially called the Islamic State in Iraq and the Levant and known as ISIL or ISIS, it made its first statement from Raqqah in May 2013 with the public execution of three civilians wrongly accused of being army officers. They were Alawites, the branch of Shiite Islam that Assad belongs to.

Mohammad, a Raqqah resident who declined to give his full name because of fear of reprisals, said people are unhappy with the strict social codes imposed by the Islamic State.

Women cannot leave home without a male guardian, shops have to close five times for prayer and people accused of theft have their hands cut off in public, he said. “People yearn for the pre-war days,” he said after arriving in Beirut. “But they’re too intimidated to speak out.”

The Islamic State yesterday killed dozens of Syrian soldiers it captured after seizing the Tabaqa military airport in Raqqah province this weekend, Rami Abdurrahman, head of the U.K.-based Syrian Observatory for Human Rights, said by phone. The observatory put the number of executions at more than 120.

A video posted online by the Unified Media Center of Raqqah showed more than 100 men in the custody of Islamic State militants forced to march in their underwear at gunpoint.

The Sunni group fought other rebels, wresting control of large areas that stretch from northern Syria to the border with Iraq in the east and killing about 2,700 fighters from other anti-Assad groups, according to the observatory.

With money from oil fields it controls in Syria and Iraq, it has managed to attract recruits. More than 6,300 mostly Syrian fighters joined the group in July, according to the observatory, which has been documenting the war through a network of activists. Syrian fighters get $400 a month, plus $50 for each child and $100 for each wife. Foreign fighters receive an additional $400 a month, it said.

Assad’s forces had engaged less with the group than other rebels partly because its brand of Islamic extremism fit the Syrian government’s narrative that terrorists are behind the insurgency against it and not activists seeking democracy.

That may change as the Islamic State digs in, said Austin Long, an assistant professor at Columbia University’s School of International and Public Affairs. The group may “push harder on the Syrian government” if it suffers military reversals across the border in Iraq, he said.

The next step for Islamic State will be to consolidate its gains and engage in activity that’s going to keep the other side off balance, such as anti-Shiite bombings in Iraq, said Bokhari, co-author of Political Islam in the Age of Democratization published last year. It also will seek to exploit the differences among rebels fighting Assad’s forces, he said.

Raqqah, about 300 kilometers northeast of the capital Damascus, became the first provincial capital to fall to the opposition in 2013. The Islamic State captured most of the province from other rebel groups earlier this year. This weekend, it completed its takeover of the province from the government when it seized the Tabaqa military airport.

Bokhari said if the Islamic State comes under U.S. aerial attack, many of the more moderate rebels may not join a war against it that could potentially boost Assad’s regime by weakening one of its main enemies.

“From the rebel point of view they don’t want a fight that strengthens the regime,” said Bokhari. “So today even if they go and fight the Islamic State, tomorrow they could have a hard time fighting the government.”