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We derive a partial electric-magnetic (PEM) duality transformation of thetwisted quantum double (TQD) model TQD$(G,\alpha)$---discrete Dijkgraaf-Wittenmodel---with a finite gauge group $G$, which has an Abelian normal subgroup$N$, and a three-cocycle $\alpha \in H^3(G,U(1))$. Any equivalence between twoTQD models, say, TQD$(G,\alpha)$ and TQD$(G',\alpha')$, can be realized as aPEM duality transformation, which exchanges the $N$-charges and $N$-fluxesonly. Via the PEM duality, we construct an explicit isomorphism between thecorresponding TQD algebras $D^\alpha(G)$ and $D^{\alpha'}(G')$ and derive themap between the anyons of one model and those of the other.

Electric-Magnetic duality in twisted quantum double model of topological orders