12 players. It was early in 5e's launch and I was running a public table, for a couple of sessions we had 12 players. It wasn't too bad, I had to recruit one of the more experienced players to co-DM and everyone at the table was under a "help the new people" requirement. So it was manageable. The table usually sat around 7-8.
I think about 10 or so, but that was for Star Trek...
We had
Captain
1st Officer
Tactical Officer
Chief Science Officer
Chief Engineering Officer (tended to go on away missions)
2nd Engineering Officer (never left the ship)
Helm
Communications
Security Chief
some other positions I can't remember.
We would however frequently split the group in two, and one person would handle the away mission stuff while another player would deal with the stuff on-board.