  A group has the (D)CI ((Directed) Cayley Isomorphism) property, or more
commonly is a (D)CI group, if any two Cayley (di)graphs on the group are
isomorphic via a group automorphism. That is, $G$ is a (D)CI group if whenever
$\rm{Cay}(G,S)\cong \rm{Cay}(G,T)$, there is some $\delta \in \rm{Aut}(G)$ such
that $S^\delta=T$. (For the CI property, we only require this to be true if $S$
and $T$ are closed under inversion.)
  Suppose $p,q,r$ are distinct odd primes. We show that $D_{2pqr}$ is a DCI
group. We present this result in the more general context of dihedral groups of
squarefree order; some of our results apply to any such group, and may be
useful in future toward showing that all dihedral groups of squarefree order
are DCI groups.
