Fusion system-relatively weakly closed not implies isomorph-normal

Statement
It is possible to have a group of prime power order $$P$$ and a subgroup $$Q$$ of $$P$$ such that $$Q$$ is a weakly closed subgroup of $$P$$ relative to any fusion system on $$P$$, but $$Q$$ is not an isomorph-normal subgroup of $$P$$: there is a subgroup of $$P$$ isomorphic to $$Q$$ that is not a normal subgroup of $$P$$.

Thus, $$Q$$ is a fusion system-relatively weakly closed subgroup and hence also a fact about::Sylow-relatively weakly closed subgroup of $$P$$ that is not an isomorph-normal subgroup.