Normal subgroup having no nontrivial homomorphism from its quotient group

Definition
A subgroup $$H$$ of a group $$G$$ is termed a normal subgroup having no nontrivial homomorphism from its quotient group if $$H$$ is a normal subgroup of $$G$$ and there is no nontrivial homomorphism of groups from the quotient group $$G/H$$ to $$H$$.

Related properties

 * Normal subgroup having no nontrivial homomorphism to its quotient group

Other incomparable properties

 * Characteristic subgroup: See no nontrivial homomorphism from quotient group not implies characteristic