Characteristic not implies normal-isomorph-free

Statement
It is possible to have a finite group $$G$$ and subgroups $$H,K$$ of $$G$$ such that $$H$$ is a characteristic subgroup of $$G$$, $$K$$ is a normal subgroup of $$G$$, and $$H,K$$ are isomorphic groups.

Facts used

 * 1) uses::Characteristic not implies characteristic-isomorph-free in finite (combined with uses::normal-isomorph-free implies characteristic-isomorph-free)
 * 2) uses::Characteristic-isomorph-free not implies normal-isomorph-free in finite (combined with uses::characteristic-isomorph-free implies characteristic)
 * 3) uses::Characteristic not implies series-isomorph-free (combined with uses::normal-isomorph-free implies series-isomorph-free)

Proof
The proof could be obtained using an example for any of the stronger facts (1)-(3).