Not exactly, Iran has a 2 tier system.
The upper tier which consists of the Council of Experts (also known as the Guardian Council) and the Supreme Leader who also control the IRGC (which controls most of Iranian industry at this point) is not another faction this is the main ruling body of Iran an the body which de-facto controls everything within it.
While the people can say elect a president the Religious leadership has veto rights into who is going to actually run basically how Iranian elections start is that you have a bunch (were talking 50 or more candidates) of candidate starting the race about half of them get rejected immediately by the religious authorities the rest "decline" to run and you end up with 1 or 2 candidates in the final race in which always one of them wins in a land slide mostly because the entire election process is fixed by the Supreme Leader.
The so call "belligerent" faction in Iran is under the direct control of the Supreme Leader and this isn't exactly a country where one does what ever they think. This is a country with well over a 1000 executions each year you won't have politicians sending out embarrassing letters or generals speaking out of term unless they want to either face a firing squad or have their necks stretched out.