partition list sets common elements

here's jist problem: given list sets, such as:

[ (1,2,3), (5,2,6), (7,8,9), (6,12,13), (21,8,34), (19,20) ]

return list groups sets, such sets have common component same group.

[ [ (1,2,3), (5,2,6), (6,12,13) ], [ (7,8,9), (21,8,34) ], [ (19,20) ] ]

note stickeyness - set (6,12,13) doesn't have common component (1,2,3), nonetheless put same organisation since (5,2,6).

to thwart matters, i should plead i don't unequivocally have neat sets, nonetheless rather db list several million rows looks like:

element | set_id
----------------
1       | 1
2       | 1
3       | 1
5       | 2
2       | 2
6       | 2

and on. i adore proceed sql, nonetheless i happy whole instruction solution.

edit: altered list buttress names (element, set_id) instead (key, group_id), terms some-more consistent. note kev's answer uses aged buttress names.