**Groups of order 36**

Here we construct a group of order 36 which has a *nonnormal*
subgroup of order 12. Let *S*_{3} denote the symmetric group of degree
3. Then is a group of order 36 which has a
normal subgroup *K* such that (e.g., we could let ). Now *S*_{3}, and hence also *G*/*K*, have a
nonnormal subgroup of order 2. Using the subgroup correspondence
theorem, we deduce that *G* has a nonnormal subgroup of order (which contains *K*), as required.

Return to

Thu Aug 1 08:14:39 EDT 1996