Retract not implies normal complements are isomorphic
Then, there may exist another normal complement to in such that is not isomorphic to .
Example of the dihedral group
Further information: dihedral group:D8
Consider the following example:
- is the dihedral group of order eight:
- is the subgroup , i.e., a two-element cyclic subgroup.
- There are two normal complements to in . The subgroup is cyclic of order four and the subgroup is a Klein-four group.