For $n \in \mathbb{N}$, $n \geq 1$, the dihedral group $D_{2n}$ is the subgroup of the orthogonal group $O(2)$ which is generated from the finite cyclic subgroup $C_n$ of $SO(2)$ and the reflection at the $x$-axis (say).
Under the further embedding $O(2)\hookrightarrow SO(3)$ the (cyclic and) dihedral groups are precisely those finite groups in the ADE classification which are not in the exceptional series.
(see e.g. Greenless 01, section 2)
The group cohomology of the dihedral group is discussed for instance at Groupprops.
Wikipedia, Dihedral group
Groupprops, Group cohomology of dihedral group:D8
John Greenlees, Rational SO(3)-Equivariant Cohomology Theories, in Homotopy methods in algebraic topology (Boulder, CO, 1999), Contemp. Math. 271, Amer. Math. Soc. (2001) 99 (web)