The rise of topology in condensed-matter physics has generated strong interest in identifying novel quantum materials in which topological protection is driven by electronic correlations. Samarium hexaboride is a Kondo insulator for which it has been proposed that a band inversion between 5d and 4f bands gives rise to topologically protected surface states. However, unambiguous proof of the existence and topological nature of these surface states is still missing, and its low-energy electronic structure is still not fully established. Here we present a study of samarium hexaboride by ultralow-temperature scanning tunneling microscopy and spectroscopy. We obtain clear atomically resolved topographic images of the sample surface. Our tunneling spectra reveal signatures of a hybridization gap with a size of about 8 meV and with a reduction of the differential conductance inside the gap by almost half, and surprisingly, several strong resonances below the Fermi level. The spatial variations of the energy of the resonances point toward a microscopic variation of the electronic states by the different surface terminations. High-resolution tunneling spectra acquired at 100 mK reveal a splitting of the Kondo resonance, possibly due to the crystal electric field.