The most common and most likely answer to this crossword clue is the 7 letter word COHORTS
I've seen this crossword clue in The Times
C
O
H
O
R
T
S
Buddy explains!

The straight part
We know that "Groups" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case groups = cohorts.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does COHORTS mean?
COHORTS noun- A group of people supporting the same thing or person.
- A demographic grouping of people, especially those in a defined age group, or having a common characteristic.
- Any division of a Roman legion, normally of about 500 men.
- An accomplice; abettor; associate.
- Any band or body of warriors.
- A natural group of orders of organisms, less comprehensive than a class.
- A colleague.
- A set of individuals in a program, especially when compared to previous sets of individuals within the same program.