The beta decay of the semimagic Sn isotopes Sn-136,Sn-137,Sn-138 has been studied at the Radioactive Isotope Beam Factory at the RIKEN Nishina Center. The first experimental information on excited states was obtained for Sb-137 while, in the case of Sb-136, the established excitation scheme could be extended by ten previously unidentified levels. In the decay of the most-neutron-rich isotope Sn-138, two gamma rays were observed for the first time. The new experimental results, in combination with state-of-the-art shell-model calculations, provide the first information with respect to the evolution of the Og(7/2) and 1d(5/2) proton single-particle states with increasing neutron number beyond N = 84.