Here's my thoughts:
The ones that emphasise the G can suggest Google, so not such a good
idea (which is a pity, but there we are) - but see also below.
The ones that use a graphic for the ".io" part don't look nice, they
make the reader think that part is being shouted. The addition of the
quote bubble to this part an make it look like JO rather than IO (No. 18
is an example of this).
Nos. 3 and 5: Not suggestive of groups (and No. 3 is hard to see).
Nos. 7 and 8: Too fussy and not intuitive. Perhaps without the graphic
No. 9: Looks like people all lying under a table.
No. 10: What does it all mean? Suggests things should happen if you
press the various bits.
No.11: Nice. Meaningless, but nice.
No. 13: The G looks like a Q.
No. 14: Is this the Post Office?
No. 15: Not as nice as No. 17.
No. 16: Q-groups? What are Q-groups?
No. 17: I like it. Simple design, can sugest the line of communication,
recognisable. The straight lines are better than the curved lines of No. 15.
No. 18: Groups.jo?
No. 20: I like this one too. Suggests a smiley face.
No. 23: EEE-groups! (What a pity that name isn't available!)
No. 32: Looks like a phone company.
If I have to vote, I will say first choice No. 17, second choice no. 20.