One of the bigger ones happened just outside of SoFi Stadium near one of the parking lots ... when a fan in a Divine Deablo jersey got thrown to the ground by a Chargers supporter rocking some Derwin James threads.

You can see in video captured by a bystander, a Maxx Crosby fan tried to step in to break things up ... but he was quickly hit in the face by not just the Raiders fan -- but a woman too.

Eventually, the Deablo fan was hit by a punch that sent him to the ground again ... and that's when the Crosby and James supporters unloaded haymakers on the man's face.

Check out the footage, the guys connected with so many blows, it actually bloodied the fan.

The woman in the fracas then got re-involved in the mix -- pulling the Crosby fan off the pile, and after a few more moments of scuffling, the Crosby supporter then body slammed her to the ground before leaving the area.

Inside the stadium, meanwhile, two Raider fans got into it with a couple Chargers backers in the seats -- leading to a flurry of punches being thrown between the men.

The fans were seemingly inspired by the action on the field, as players between the two squads got into a spat late in Sunday's contest ... with Chargers receiver Joshua Palmer and Raiders cornerback Jack Jones both ejected for their roles in the tussle.