Left-transitively WNSCDIN not implies normal

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., left-transitively WNSCDIN-subgroup) need not satisfy the second subgroup property (i.e., normal subgroup)
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Statement

We can have a group $G$ and a left-transitively WNSCDIN-subgroup $H$ of $G$ that is not normal in $G$.

Proof

Example of a subgroup of order two

Further information: dihedral group:D8

Let $G$ be any group with a non-normal subgroup $H$ of order two. Then, $H$ is left-transitively WNSCDIN in $G$.

For a concrete example, take $G$ to be a dihedral group and $H$ to be a subgroup of order two generated by a reflection element.