Isomorph-conjugacy is normalizer-closed in finite

This article gives the statement and possibly, proof, of a subgroup property satisfying a subgroup metaproperty, when the big group is a finite group. That is, it states that in a Finite group (?), the subgroup property (i.e., Isomorph-conjugate subgroup (?)) satisfies the metaproperty (i.e., Normalizer-closed subgroup property (?))
View all subgroup metaproperty satisfactions in finite groups $|$ View all subgroup metaproperty satisfactions in finite groups $|$ View all subgroup metaproperty satisfactions $|$ View all subgroup metaproperty dissatisfactions

Statement

The normalizer of an isomorph-conjugate subgroup in a finite group is again isomorph-conjugate.

Facts used

1. Normalizer of isomorph-conjugate implies isomorph-dominating
2. Isomorph-dominating equals isomorph-conjugate in finite

Proof

The proof follows by piecing together facts (1) and (2).