There was sometimes disorder between supporters of different gladiators, such as when Pompeii was banned from having gladiator games for ten years due to a riot between locals and people from the countryside. More often, though, riots happened due to the chariot races, which were more team-oriented - and even then, the riots were more common in Constantinople than in Rome, which was, by the time of the Empire, heavily garrisoned with paramilitary forces.
There was sometimes disorder between supporters of different gladiators, such as when Pompeii was banned from having gladiator games for ten years due to a riot between locals and people from the countryside. More often, though, riots happened due to the chariot races, which were more team-oriented - and even then, the riots were more common in Constantinople than in Rome, which was, by the time of the Empire, heavily garrisoned with paramilitary forces.
Here’s a particularly notable one:
https://en.m.wikipedia.org/wiki/Nika_riots