Isomorph-freeness is quotient-transitive

Statement with symbols
If $$H \le K \le G$$ are such that $$H$$ is an isomorph-free subgroup of $$G$$ and $$K/H$$ is an isomorph-free subgroup of $$G/H$$, then $$K$$ is an isomorph-free subgroup of $$G$$.