BAGHDAD — As fighters for the Islamic State in Iraq and Syria continue to seize territory, the group has quietly built an effective management structure of mostly middle-aged Iraqis overseeing departments of finance, arms, local governance, military operations and recruitment.

At the top the organization is the self-declared leader of all Muslims, Abu Bakr al-Baghdadi, a radical chief executive officer of sorts, who handpicked many of his deputies from among the men he met while a prisoner in American custody at the Camp Bucca detention center a decade ago.

He had a preference for military men, and so his leadership team includes many officers from Saddam Hussein’s long-disbanded army.

They include former Iraqi officers like Fadel al-Hayali, the top deputy for Iraq, who once served Mr. Hussein as a lieutenant colonel, and Adnan al-Sweidawi, a former lieutenant colonel who now heads the group’s military council.