Join of 4-subnormal subgroup and finite subnormal subgroup need not be subnormal

Statement
It is possible to have a group $$G$$, a fact about::4-subnormal subgroup $$H$$ of $$G$$, and a fact about::finite subnormal subgroup $$K$$ of $$G$$, such that the join $$\langle H, K \rangle$$ is not a subnormal subgroup.

Similar facts

 * 4-subnormal not implies finite-conjugate-join-closed subnormal

Opposite facts

 * Join of 3-subnormal and finite subnormal implies subnormal