[seqfan] When are stereoisomers counted in A000628?

[Natan Consigli]

Dear seqfans,
I've come across this sequence and in the comments section it is
written: "Regarding
stereoisomers as different means that only the alternating group A_4 acts
at each node, not the full symmetric group S_4."
I could be wrong, but isn't it supposed to be the other way around?
What I mean is: "stereoisomers are counted as different every time the
symmetric group S_4 acts on some node".

Regards
Natan Consigli