This provides
1) a different proof of the AMM pushout diagram for M12 at p=2
and
2) and uses it to construct a map BM12 --> BG_2 that geometrically
realizes the module structure of H^*(BM12,Z/2) over the rank 3
Dickson invariants.
3) Briefly discusses a possible similar picture for the Conway
   'dot 3" group Co(3) and the rank 4 Dickson invariants.