Use the subgroup lattice of to help find the normalizers (1) and (2) .
We computed the subgroup lattice of in this previous exercise.
- (Note that .) We have , so that this normalizer is either , , or .
Note that , so that , but . So .
- We have , so that this normalizer is either , , or .
Now . Note that is in this normalizer since , , and . However, is not in this normalizer since . So .