  In this paper we study the (Cohen-Macaulay) type of orders over Dedekind
domains in \'etale algebras. We provide a bound for the type, and give formulas
to compute it. We relate the type of the overorders of a given order to the
size of minimal generating sets of its fractional ideals, generalizing known
results for Gorenstein and Bass orders. Finally, we give a classification of
the ideal classes with multiplicator ring of type $2$, with applications to the
computations of the conjugacy classes of integral matrices and the isomorphism
classes of abelian varieties over finite fields.
