In 2D, the symmetry group Dn includes reflections in lines.
With reflection symmetry in a plane perpendicular to the n-fold rotation axis, we have Dnh, [n], (*22n).
Dnd (or Dnv), [2n,2+], (2*n) has vertical mirror planes between the horizontal rotation axes, not through them.
Dn is the symmetry group of a partially rotated prism.
n = 1 is not included because the three symmetries are equal to other ones: For n = 2 there is not one main axis and two additional axes, but there are three equivalent ones.