Normal-isomorph-containing subgroup

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a normal-isomorph-containing subgroup if $$H$$ is a defining ingredient::normal subgroup of $$G$$, and for any normal subgroup $$K$$ of $$G$$ isomorphic to $$H$$, $$K$$ is contained in $$H$$.