  We describe the structure, including composition factors and submodule
lattices, of cross-characteristic permutation modules for the natural actions
of the orthogonal groups $O_{m}^{\pm}(3)$ with $m\geq6$ on nonsingular points
of their standard modules. These actions together with those studied in
\cite{HN} are all examples of primitive rank 3 actions of finite classical
groups on nonsingular points.
