This image made from video posted on a militant website July 5, 2014, which has been authenticated based on its contents and other AP reporting, purports to show the leader of the Islamic State group, Abu Bakr al-Baghdadi, delivering a sermon at a mosque in Iraq. (AP Photo/Militant video)

While it's tempting to imagine them as a disorganized horde, the reality of the Islamic State -- the extremist Islamist group who have taken over vast swathes of Syria and Iraq -- is that the sheer scale of their military operations, not to mention their Caliphate ambitions, are not possible without some kind of organized leadership structure.

In a new report on Islamic State, the Soufan Group has broken down graphically what we know about ISIS's leadership structure. It's a fascinating glimpse of how the group that has captured so much of the world actually operates.

We'll break it out further (if the chart is hard to read, please check the pdf of Soufan Group's full report).

(The Soufan Group / PBS Frontline)

First, there's the leadership. At the top there is the Caliph, Abu Bakr al Baghdadi (also known as Ibrahim Awad Ibrahim al Badri al Samarrai), who is no doubt the best known member of the Islamic State so far. He is the overall leader of the Islamic State.

The Soufan Group then points to two other men: Abu Muslim al Turkmani (Fadil Ahmad Abdallah al Hayyali) who oversees Islamic State in Iraq, and Abu Ali al Anbari, who oversees it in Syria. Both of these men are former members of the Iraqi Ba'ath party, the report notes.

Turkmani and Anbari are believed to be members of the Shura Council, the Islamic State's highest advisory body. In theory, Baghdadi must run decisions past the Shura Counil, which could dismiss the Caliph if it he fails to carry out his duties. The council is headed by Abu Arkan al Ameri and has nine to 11 members, all of whom are believed to be from Iraq. Another possible member of the Shura Council is Omar al Shishani  (a.k.a Tarkhan Tayumurazovich Batirashvili), a well-known ethnic Chechen who is distinctive for his red beard and reports of his fighting prowess (the Soufan Group cast some doubt on whether Shishani, a military commander, is a member of the council however).

The most powerful body of the Islamic State, however, is the Sharia Council, which is said to have six members. It is the body that selects the Caliph and oversees Sharia law. The Islamic State is also said to have recruited a number of religious scholars to help its boost its legitimacy.

(The Soufan Group / PBS Frontline)

Below that level are the other, less important councils. For example, there's the Security and Intelligence Council, designed to maintain Abu Bakr's control and stop any plots against him. Then there's the Military Council, designed to help fight external forces, and the Provincial Council deals with civilian administration of the Islamic State's 18 provinces (it is led by Turkmani, and each province has a governor known as a Wali).

The Finance Council, the Media Council, and the Religious Affairs Council are self-explanatory, and the Soufan Group also believes there may also a council dedicated to looking after soldiers and their families.

(The Soufan Group / PBS Frontline)

Finally, the Soufan Group highlights a number of officials who have specific roles in the Islamic State. Abdul Rahman al Afari is a member of the military council who is responsible for the families of dead shoulders, for example, while Abdulla Ahmad al Mishhadani coordinates guest houses for foreign fighters. Abu Yahya al Iraqi is with Baghdadi at all times and acts as a channel between the Caliph and Abu Ali al Anbari.

Such a leadership structure may seem complicated, but given the size of the land the Islamic State has, plus the number of soldiers it now has (as many as 31,500 according to CIA estimates), such a leadership apparatus is probably necessary. What's more alarming is that, as Soufan Group readily admit, the scope of what we know about the Islamic State's leadership is limited and hard to verify. "Even if a report is accurate one day, it may change the next," the Soufan Group's report notes.