  We construct new examples of immersed minimal surfaces with catenoid ends and
finite total curvature, of both genus zero and higher genus. In the genus zero
case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry
group the natural $\bfZ_2$ extension of the dihedral group $D_n$. The surfaces
are constructed by proving existence of the conjugate surfaces. We extend this
method to cases where the conjugate surface of the fundamental piece is
noncompact and is not a graph over a convex plane domain.
