Hesitant fuzzy subgroup defined on a group G generalizes the idea of fuzzy subgroups. It mainly focuses on the multiplicity of values encountered when dealing with hesitant fuzzy sets. The preliminary concepts needed to build Hesitant fuzzy groups are discussed in this paper. Some results using the extension principle for hesitant fuzzy sets are discussed. The extension principle uses a new conjunction and disjunction operation on hesitant fuzzy sets. Various properties of composition and inverse operations on hesitant fuzzy sets are discussed before studying the structure of hesitant fuzzy groups. The concept of normal hesitant fuzzy subgroup of a group G is also studied in detail