  We consider a class of quasi-Hopf algebras which we call \emph{generalized
twisted quantum doubles}. They are abelian extensions $H = \mb{C}[\bar{G}]
\bowtie \mb{C}[G]$ ($G$ is a finite group and $\bar{G}$ a homomorphic image),
possibly twisted by a 3-cocycle, and are a natural generalization of the
twisted quantum double construction of Dijkgraaf, Pasquier and Roche. We show
that if $G$ is a subgroup of $SU_2(\mb{C})$ then $H$ exhibits an orbifold McKay
Correspondence: certain fusion rules of $H$ define a graph with connected
components indexed by conjugacy classes of $\bar{G}$, each connected component
being an extended affine Diagram of type ADE whose McKay correspondent is the
subgroup of $G$ stabilizing an element in the conjugacy class. This reduces to
the original McKay Correspondence when $\bar{G} = 1$.
