# Groups embeddable as normal subgroups in a finite group with isomorphic complements

From Groupprops

## Definition

Suppose and are finite groups. We say that and are **embeddable as normal subgroups in a finite group with isomorphic complements** if there exists a finite group with normal subgroups and subgroups such that:

- is isomorphic to .
- and are permutable complements: in particular, is an internal semidirect product of and .
- is isomorphic to .
- and are permutable complements: in particular, is an internal semidirect product of and .
- is isomorphic to .