Let D be an integral domain with Spec(D) finite, K the quotient field of D, [D,K] the set of rings between D and K, and SFc(D) the set of semistar operations of finite character on D. It is well known that |Spec(D)| ${leq}$ |SFc(D)|. In this paper, we prove that |Spec(D)| = |SFc(D)| if and only if D is a valuation domain, if and only if |Spec(D)| = |[D,K]|. We also study integral domains D such that |Spec(D)|+1 = |SFc(D)|.