No. This site uses a lot of fan created characters, and with them, clans have been created as well. The official groups I know are as follows. I'm not going to count obvious groups like the Earthrealm heroes or Shao Kahn's army.

Lin Quei- Chinese assasins for hire, and enemies of the Shirai Ryu. Tried to create cyber ninjas during the Earthrealm invasion. Have recently been reformed as heroes with the younger Sub Zero taking leadership.

Order of Light/White Lotus Society- Heroic Shaolin warriors devoted to protecting Earthrealm from invasion. The original hosts of Mortal Kombat, before Shang Tsung took the tournament over. Shao Kahn came close to destroying them once, but didn't succeed.

Black Dragon (1)- Criminal organisation, originally formed of ex Red Dragon members, causing the two clans to hate one another. Through the Red Dragon and Special Forces, they have now been destroyed.

US Special Forces- Originally only sent to capture Kano, but Sonya and Jax had since become vital to the fight for protecting Earth. After the invasion, Sonya forms the Outworld Investigation Agency.

Shirai Ryu- Japanese ninja clan, founded by Takeda, and rivals to the Lin Quei. In his life, Scorpion was a member of this clan until they were all eliminated by Quan Chi.

Brotherhood of Shadow- Led by Shinnok, these are Netherrealm demons who have included Quan Chi, Sareena and Reiko. Not much known about these guys, or whether they are still around.

Red Dragon- Centuries old crime clan, now led by Mavado. Succeeded in destroying their rivals the Black Dragon, before Kabal started building a new clan. Clan's existance only revealed recently to the wider world.

Black Dragon (2)- A surviving Kabal restarted the clan under Havik's guidance. Unlike the old clan, these guys are more random looters fighting for chaos, than organised criminals.

Elder Gods- Responsible for watching over Earthrealm, and using champions to fight for them. Both Raiden and Shinnok were once Elder Gods.

Tekunin- Cyborg clan formed by Sektor to take over Japan. Note, this clan might not be canon in the storyline.

Seidan Guard- They uphold the strict laws and protect the Orderrealm. Hotaru is a high ranking member, and both Dairou and Shujinko were part of it at one point.

Resistance- Doesn't have an official name yet, but worth a mention I think. Darrius leads the resistance in the Orderrealm, with help from Havik and Dairou.

Wow, that deserves some dragon points, thanks dude.