Fatah has always regarded the PLO as its own organization. They have the largest faction inside the PLO.
The PLO includes:
Fatah - Largest faction.
The Popular Front for the Liberation of Palestine (PFLP) - Second largest.
The Democratic Front for the Liberation of Palestine (DFLP) - Third largest.
The Palestinian People's Party (PPP).
As-Sa'iqa.
The Palestine Democratic Union (Fida).
The Palestinian Popular Struggle Front (PPSF).
The Palestinian Arab Front (PAF).

All besides Fatah are neutral in the fighting. And even inside Fatah there are split factions (not under the control of Mahmud Abbas)!