This paper characterizes binary trees with n leaves, which have the greatest number of subtrees. These binary trees coincide with those which were shown by Fischermann et al. [Wiener index versus maximum degree in trees, Discrete Appl. Math. 122(1–3) (2002) 127–137] and Jelen and Triesch [Superdominance order and distance of trees with bounded maximum degree, Discrete Appl. Math. 125 (2–3) (2003) 225–233] to minimize the Wiener index.