[r-t] Group thy. again

[Robin Woolley]

Hi All,

RAS asks for a definition of 'obvious'. The word here depends upon whether 
A4 is the only subgroup of S4 of size 12.

I had conjectured that the group I sought of this order might have equal 
numbers of odd and even rows, but , following RAS's note, I found on the 
internet that A4 is the unique largest subgroup of S4. (The group I had in 
mind was something *like* D6 - not D6 itself, obviously - which has 12 
members)

Today's question generalises this. Given any group Sn, is An unique of all 
the subgroups of size n!/2? (i.e., the only one.)

Best wishes
Robin