Ice is ubiquitous in nature, and heterogeneous ice nucleation is the most common pathway of ice formation. How surface properties affect the propensity to observe ice nucleation on that surface remains an open question. We present results of molecular dynamics studies of heterogeneous ice nucleation on model surfaces. The models surfaces considered emulate the chemistry of kaolinite, an abundant component of mineral dust. We investigate the interplay of surface lattice and hydrogen bonding properties in affecting ice nucleation. We find that lattice matching and hydrogen bonding are necessary but not sufficient conditions for observing ice nucleation at these surfaces. We correlate this behavior to the orientations sampled by the metastable supercooled water in contact with the surfaces. We find that ice is observed in cases where water molecules not only sample orientations favorable for bilayer formation but also do not sample unfavorable orientations. This distribution depends on both surface-water and water water interactions and can change with subtle modifications to the surface properties. Our results provide insights into the diverse behavior of ice nucleation observed at different surfaces and highlight the complexity in elucidating heterogeneous ice nucleation.