Algebra Normal Subroups I have a question about normal subgroups of index $2$:
If $H$ is a normal subgroup of $G$ of index $2$, is there anything that we can say about $G$?

If $H$ is Abelian you can build all $G$'s using 2nd cohomology group $H^2(\mathbb{Z}_2,H)$. 
If $H$ is non-Abelian you can figure out by  $H^3(\mathbb{Z}_2,Z(H))$ wheter there is such $G$.
For details see K.Brown, Cohomology of Groups.
