Strongly embedded subgroup

Symbol-free definition
A subgroup of a group is termed strongly embedded or tightly embedded if it has even order, is self-normalizing and its intersection with any other conjugate has odd order.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed strongly embedded or tightly embedded in $$G$$ if $$H$$ has even order and for any $$x$$ in $$G$$ which is not in $$H$$, $$H$$ &cap; $$H^x$$ has odd order.

Stronger properties

 * Malnormal subgroup

Weaker properties

 * Self-normalizing subgroup

Opposites

 * Normal subgroup

Metaproperties
The condition of having even order is clearly transitive, while the condition of the intersection with any conjugate having odd order is also transitive.