  Let K be a knot of genus g. If K is fibered, then it is well known that the
knot group pi(K) splits only over a free group of rank 2g. We show that if K is
not fibered, then pi(K) splits over non-free groups of arbitrarily large rank.
Furthermore, if K is not fibered, then pi(K) splits over every free group of
rank at least 2g. However, pi(K) cannot split over a group of rank less than
2g. The last statement is proved using the recent results of Agol,
Przytycki-Wise and Wise.
