Isomorph-automorphic normal subgroup

Definition
A subgroup of a group is termed an isomorph-automorphic normal subgroup if it satisfies the following two conditions:


 * 1) It is a normal subgroup.
 * 2) Every subgroup of the whole group isomorphic to it is an automorphic subgroup, i.e., there is an automorphism sending one subgroup to the other.