What are some words in English that mean something like "groups of people working together"?

Collaboration, and it's synonyms.

Off the top of my head: team, band, party, cooperative, crew, gang, brother/sisterhood, alliance.

I’m not a native speaker, but the following come in mind: crew, team, ring, syndicate, tandem, gang, allied, collaborate,

“Orgies.”

"Chain gang"