Dreadful part of a family terrorist group (5)

I believe the answer is:

mafia

I'm a little stuck... Click here to teach me more about this clue!

'group' is the definition.
The answer is an example.

I cannot understand how the rest of the clue works.

(Other definitions for mafia that I've seen before include "Secret criminal organisation" , "Criminal organisation also known as Cosa Nostra" , "Sicilian criminal organisation" , "Sicilian criminals" , "Sicilian secret society" .)

I've seen this clue in The Globe and Mail.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.