  We show that given a $G$-structure $P$ on a differentiable manifold $M$, if
the group $G(M)$ of automorphisms of $P$ is big enough, then there exists the
quotient of an stochastic flows $phi_t$ by $G(M)$, in the sense that $\phi_t =
\xi_t \circ \rho_t$ where $\xi_t \in G(M)$, the remainder $\rho_t$ has
derivative which is vertical but transversal to the fibre of $P$. This
geometrical context generalizes previous results where $M$ is a Riemannian
manifold and $\phi_t$ is decomposed with an isometric component, see Liao
\cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds to
the particular case of an SO(n)-structure on $M$.
