Series-equivalent subgroups

Definition
Suppose $$G$$ is a group and $$H$$ and $$K$$ are normal subgroups. We say that $$H$$ and $$K$$ are series-equivalent if $$H$$ and $$K$$ are isomorphic groups and the quotient groups $$G/H$$ and $$G/K$$ are isomorphic groups.

Stronger properties

 * Equal subgroups
 * Weaker than::Conjugate subgroups
 * Weaker than::Automorphic subgroups

Weaker properties

 * Isomorphic subgroups
 * Quotient-isomorphic subgroups