We introduce an order on the set of nondivisorial ideals of a numerical semigroup S, and link antichains of this order with the star operations on S; subsequently, we use this order to find estimates on the number of star operations on S. We then use them to find an asymptotic estimate on the number of nonsymmetric numerical semigroups with n or less star operations, and to determine these semigroups explicitly when n = 10.
