Double coset index two implies maximal

Statement
If the fact about::double coset index of a subgroup in a group is two, i.e., if the subgroup has precisely two double cosets, then the subgroup is a fact about::maximal subgroup.

Related facts

 * Index three implies normal or double coset index two
 * Index four implies 2-subnormal or double coset index two

Proof idea
The idea is that any intermediate subgroup containing the given subgroup must be a union of double cosets of the subgroup.