Robbery, fencing, protection and extortion, termination, prostitution, gambling, smuggling and distribution, loansharking, lobbying, counter-intelligence, and conflict resolution.
Robbery being the theft of items.
Fencing is the selling of items previously stolen.
Extortion is gaining money or other resources in exchange for threats. Protection is when the threat is violence perpetrated by the one making the threat. Blackmail is also a specific kind of extortion.
Termination is assassination (for hire) or enforcement (of the rules or for breaking agreements).
Prostitution is sex for hire.
Gambling is where one places money on a possibility. If the possibility occurs, you get money back. If not, you don't. This could be a sporting event, a card game, a roulette wheel, or any other possibility.
Smuggling and distribution is the transport and sale of illegal items.
Loansharking is the offer of loans, often to people with little collateral or income but at high rate of interest.
Lobbying is the attempt to influence the legal government. It may include bribes, blackmail, or extortion.
Counter-intelligence would be the search for people who might be sharing information with law enforcement.
Conflict resolution is when two or more mafia members disagree. They can bring their dispute to conflict resolution where it can be mediated or arbitrated.
It would also be reasonable to have a budgetary committee, just as a regular legislature would. You may also consider giving the jobs more mafia names like Boss Pimp, Viglord, whacking, hooking, etc.