Abnormal normalizer not implies pronormal

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., subgroup with abnormal normalizer) need not satisfy the second subgroup property (i.e., pronormal subgroup)
View a complete list of subgroup property non-implications | View a complete list of subgroup property implications
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EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property subgroup with abnormal normalizer but not pronormal subgroup|View examples of subgroups satisfying property subgroup with abnormal normalizer and pronormal subgroup

Statement

A subgroup whose normalizer is an abnormal subgroup need not be pronormal.

Facts used

1. Abnormal normalizer and 2-subnormal not implies normal
2. Pronormal and subnormal implies normal

Proof

The proof follows directly by combining facts (1) and (2).