Using the spectroscopic catalogue of the Sloan Digital Sky Survey Data Release 10, we have explored the abundance of satellites around a sample of 254 massive (1011 < M⋆ < 2 × 1011 M⊙) local (z < 0.025) galaxies. We have divided our sample into four morphological groups (E, S0, Sa, Sb/c). We find that the number of satellites with M⋆ ≳ 109 M⊙ and R < 300 kpc depends drastically on the morphology of the central galaxy. The average number of satellites per galaxy host (NSat/NHost) down to a mass ratio of 1:100 is 4.5 ± 0.3 for E hosts, 2.6 ± 0.2 for S0, 1.5 ± 0.1 for Sa and 1.2 ± 0.2 for Sb/c. The amount of stellar mass enclosed by the satellites around massive E-type galaxies is a factor of 2, 4 and 5 larger than the mass in the satellites of S0, Sa and Sb/c types, respectively. If these satellites would eventually infall into the host galaxies, for all the morphological types, the merger channel will be largely dominated by satellites with a mass ratio satellite-host μ > 0.1. The fact that massive elliptical galaxies have a significant larger number of satellites than massive spirals could point out that elliptical galaxies inhabit heavier dark matter haloes than equally massive galaxies with later morphological types. If this hypothesis is correct, the dark matter haloes of late-type spiral galaxies are a factor of ˜2-3 more efficient on producing galaxies with the same stellar mass than those dark matter haloes of early-type galaxies.