  The fundamental quandle is a powerful invariant of knots, links and spatial
graphs, but it is often difficult to determine whether two quandles are
isomorphic. One approach is to look at quotients of the quandle, such as the
$n$-quandle defined by Joyce \cite{JO}; in particular, Hoste and Shanahan
\cite{HS2} classified the knots and links with finite $n$-quandles. Mellor and
Smith \cite{MS} introduced the $N$-quandle of a link as a generalization of
Joyce's $n$-quandle, and proposed a classification of the links with finite
$N$-quandles. We generalize the $N$-quandle to spatial graphs, and investigate
which spatial graphs have finite $N$-quandles. We prove basic results about
$N$-quandles for spatial graphs, and conjecture a classification of spatial
graphs with finite $N$-quandles, extending the conjecture for links in
\cite{MS}. We verify the conjecture in several cases, and also present a
possible counterexample.
