Index three implies normal or double coset index two
From Groupprops
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property must also satisfy the second subgroup property
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Statement
Any 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.