A nonperturbative close-coupling technique is used to calculate differential cross sections for the electron-impact ionization of H2 at an energy of 35.4 eV. Our approach allows cross sections for any orientation of the molecule with respect to the incident electron beam to be analyzed. New features in the resulting cross sections are found compared with the case where the molecular orientation is averaged, and also with cross sections for He at equivalent electron kinematics. When averaged over all possible molecular orientations, good agreement is found with recent experimental results.