  Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter
community, in part because they represent topological phases of matter, but
also because they characterize the response theory of certain symmetry
protected topological (SPT) phases. However, as yet there has not been a
comprehensive treatment of the spectra of these models in the field theoretic
setting -- the goal of this work is to fill the gap in the literature, at least
for a selection of DW models with abelian gauge groups but non-abelian
topological order. As applications, various correlation functions and fusion
rules of line operators are calculated. We discuss for example the appearance
of non-abelian statistics in DW theories with abelian gauge groups.
