  The fundamental quandle is a powerful invariant of knots and links, but it is
difficult to describe in detail. It is often useful to look at quotients of the
quandle, especially finite quotients. One natural quotient introduced by Joyce
is the $n$-quandle. Hoste and Shanahan gave a complete list of the knots and
links which have finite $n$-quandles for some $n$. We introduce a
generalization of $n$-quandles, denoted $N$-quandles (for a quandle with $k$
algebraic components, $N$ is a $k$-tuple of positive integers). We conjecture a
classification of the links with finite $N$-quandles for some $N$, and we prove
one direction of the classification.
