Index four implies 2-subnormal or double coset index two

Statement
Any fact about::subgroup of index four (i.e., a subgroup of a group whose index in the whole group is four) is either 2-subnormal or has double coset index two.

Related facts

 * Subgroup of index two is normal
 * Subgroup of least prime index is normal
 * Index three implies normal or double coset index two