Hall does not satisfy transfer condition

Statement
It is possible to have a finite group $$G$$, a Hall subgroup $$H$$, and a subgroup $$K$$ of $$G$$ such that $$H \cap K$$ is not a Sylow subgroup of $$K$$.

Related facts

 * Sylow does not satisfy transfer condition
 * Hall satisfies intermediate subgroup condition

Facts used

 * 1) Hall satisfies transitivity
 * 2) Transitive and transfer condition implies intersection-closed
 * 3) Hall is not intersection-closed

Property-theoretic proof
The proof follows directly by combining facts (1), (2), and (3).