General help

I think, yes, a group can belong to many groupings. A grouping is collection of groups or even one group only that is encased in an invisibility cloak so others cannot see its work
So you can have
group A and Group B inside grouping 1
Group B and Group C inside grouping 2
Group A and Group C inside grouping 3
I have never tried this though and you might get odd results in terms of what each group sees and doesn't see - but as far as I know, you can do this.

Hi there
As Mary indicates, this is definitely possible. A group can belong to many groupings like a student can belong to many groups. Which I guess you could take to a student can belong to many groups and groupings!!

It is important if you use the groups in different groupings to ensure the correct grouping is assigned for the resource/activity. This will ensure only the relevant groups are used and seen for the activity (eg the forum visible groups drop down list would only display the groups belong to the grouping specified in the forum settings).

I hope this helps clarify
Cheers
Teresa