There are numerous crime syndicates operating galaxy wide, many of their operations are considered illegal under both the Galactic Republic and the Sith Empire; these include slavery, contract killings, smuggling and spice dealing. The two largest are the Hutt Cartel and the human centric Exchange syndicate.
List of crime syndicates
Centered on Hutta and it's moon Nar Shaddaa the Hutt Cartel is one of the galaxy's two largest crime syndicates. Its power structure is divided between several powerful Hutt leaders competing against one another for wealth and territory. 300 years ago the Cartel's power was in sharp decline with its largest rival, the Exchange, all but controlling Nar Shaddaa. The Cartel managed to claw back power after the Visionary, the Exchange's centre of operations of Nar Shaddaa, was destroyed it's sector chief, G0-T0, went missing.
Lead by the mysterious Compeer the Exchange is one of the two largest crime syndicates in the galaxy. Unlike the Hutt Cartel the Exchange has a stricter chain of command with its leaders answering to one man and not competing directly with one another. During the Jedi Civil War and the subsequent Dark War the Exchange had allied it's self indreicly with the Sith Empire and Czerka Corporation which gave it a presence on worlds throughout both the Empire and the Galactic Republic making it the galaxy's largest syndicate.
The Exchange suffered massive blows during the Jedi Civil War when Taris was destroyed by the Sith Empire and disruption of its operations on Nar Shaddaa during the Dark War, the latter of which took years for them to recover allowing the Cartel to move in on their territory.
The Black Sun is a smaller syndicate and is known to control areas on Corsucant. It is unknown whether it works with or against either of its two far larger rivals.