Due to its p-like character, the valence band in GaAs-based heterostructures offers rich and complex spindependent phenomena. One manifestation is the large anisotropy of Zeeman spin splitting. Using undoped, coupled quantum wells (QWs), we examine this anisotropy by comparing the hole-spin dynamics for high-and low-symmetry crystallographic orientations of the QWs. We directly measure the hole g factor via time-resolved Kerr rotation, and for the low-symmetry crystallographic orientations (110) and (113a), we observe a large in-plane anisotropy of the hole g factor, in good agreement with our theoretical calculations. Using resonant spin amplification, we also observe an anisotropy of the hole-spin dephasing in the (110)-grown structure, indicating that crystal symmetry may be used to control hole-spin dynamics.