I have a permutation group, e.g.

g=PermutationGroup[{Cycles[{{1, 2}}]}]

but not necessarily limited to a single generating cycle.

What I want is to create a list of subsets of some integers, for instance {1,2,3}, modulo this group g. I know I can create all subsets of this list of, say, length 2, via

Subsets[{1,2,3},{2}] (*  == {{1, 2}, {1, 3}, {2, 3}}  *)

Under the action of g, the last two items are considered equivalent, as one can map 1<->2.

How do I do this, ideally without filtering a list of all possible subsets (as those blow up exponentially when the list of integers becomes longer)?

Thanks a lot!

/J