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By adapting the notion of chirality group, the duality group of $\cal H$ canbe defined as the the minimal subgroup $D({\cal H}) \trianglelefteq Mon({\calH})$ such that ${\cal H}/D({\cal H})$ is a self-dual hypermap (a hypermapisomorphic to its dual). Here, we prove that for any positive integer $d$, wecan find a hypermap of that duality index (the order of $D({\cal H})$), evenwhen some restrictions apply, and also that, for any positive integer $k$, wecan find a non self-dual hypermap such that $|Mon({\cal H})|/d=k$. This $k$will be called the \emph{duality coindex} of the hypermap.

Duality index of oriented regular hypermaps