Index three implies normal or double coset index two

Statement
Any fact about::subgroup of index three (i.e., a subgroup of a group whose index is three), is either normal or has double coset index two: it has exactly two double cosets.

Related facts

 * Subgroup of index two is normal
 * Index four implies 2-subnormal or double coset index two
 * Subgroup of least prime index is normal