Potentially characteristic not implies normal-extensible automorphism-invariant

Statement
A potentially characteristic subgroup of a group need not be a normal-extensible automorphism-invariant subgroup.

Facts used

 * 1) uses::Normal not implies normal-extensible automorphism-invariant in finite: Actually, we need a slightly stronger version of this statement. Namely, we need that there is a normal-extensible automorphism of a finite group that is not a normal automorphism. The example given in the proof is a finite group, so the proof actually shows the stronger version.
 * 2) uses::Finite normal implies potentially characteristic, or, alternatively, uses::Finite NPC theorem

Proof
The proof follows directly from facts (1) and (2).