The fundamental science question we address in this research concerns the evolution of asteroid families; more specifically, does asteroid (6) Hebe have a genetic family, and does this genetic family provide insight into the structure of (6) Hebe? Hebe has been identified dynamically and spectroscopically as the H-chondrite parent body. The H chondrites exhibit a range of metamorphisms suggesting deep excavation from the parent body, an event expected to form a family. Previously, several small H-type asteroids were identified near Hebe, supporting this possibility, but they were insufficient to test its existence. We initiated a limited spectroscopic investigation of 36 asteroids near Hebe between 2009 and 2018 using the NASA Infrared Telescope Facility’s SpeX instrument to test for the presence of a small dynamical family of H-chondrite composition. Of our 36 asteroid spectra, 16 were featureless, 1 contained a single absorption feature, 16 exhibited two absorption features, and 3 were deemed unusable due to poor quality. Our interpretation of asteroid spectra with two absorption features began with the extraction and interpretation of band centers and the band area ratio, which we used to determine the surface mineralogy. In this paper, we report on the nine asteroids that were determined to have an H-chondrite mineralogy. We conclude that asteroids with H-chondrite mineralogies reside on both sides of the 3:1 Kirkwood gap, and this implies that (6) Hebe does have an old-dispersed family, as well as provide spectral evidence for Bottke’s hypothesis of resonance jumping.