It's very complex

Ali Khedery looks at the number of factions involved in Iraq - and there a lot, none of which is Simon pure. The Sunnis have five groups and 6,000,000 defenders. The Shiites have nine groups and 15,000,000 Iraqis. It is a frightening and complex analysis. Khedery concludes:

As you can see, Iran has tens of thousands of loyal, capable, highly trained proxies available to them in Iraq, all of which were involved in attacking U.S. forces in Iraq during the war. Though the capabilities differ between these groups, all are loyal to Iran and continue to operate under IRGC-QF direction and guidance and will lead Iran's fight against ISIS and Sunni extremists as events unfold in Iraq. Many of these proxy groups are also integrated into Iraq's Security Forces (army and police) which makes them more than just a militia. They are a force multiplier with quasi-Iraqi governmental status fighting not only on behalf of Iran, but fully sanctioned by the Iraqi government.