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Abstract  As a consequence of a general result about finite group actions on 3‐manifolds, we show that a hyperbolic 3‐manifold can be the cyclic branched cover of at most fifteen inequivalent knots inS   3    (in fact, a main motivation of the present paper is to establish the existence of such a universal bound). A similar, though weaker, result holds for arbitrary irreducible 3‐manifolds: an irreducible 3‐manifold can be a cyclic branched cover of odd prime order of at most six knots inS   3   . We note that in most other cases such a universal bound does not exist.

Finite group actions on 3‐manifolds and cyclic branched covers of knots