  Automorphic loops are loops in which all inner mappings are automorphisms. A
large class of automorphic loops is obtained as follows: Let $m$ be a positive
even integer, $G$ an abelian group, and $\alpha$ an automorphism of $G$ that
satisfies $\alpha^2=1$ if $m>2$. Then the dihedral-like automorphic loop
$\mathrm{Dih}(m,G,\alpha)$ is defined on $\mathbb Z_m\times G$ by
$(i,u)(j,v)=(i+j, ((-1)^{j}u+v)\alpha^{ij})$. We prove that two finite
dihedral-like automorphic loops $\mathrm{Dih}(m,G,\alpha)$,
$\mathrm{Dih}(\overline{m},\overline{G},\overline{\alpha})$ are isomorphic if
and only if $m=\overline{m}$, $G=\overline{G}$, and $\alpha$ is conjugate to
$\overline{\alpha}$ in the automorphism group of $G$. Moreover, for a finite
dihedral-like automorphic loop $Q$ we describe the structure of the
automorphism group of $Q$ and its subgroup consisting of inner mappings of $Q$.
