We have grown epitaxial LaFeO3 thin films on different oxide substrates by molecular beam epitaxy and investigated them using transmission electron microscopy. The films reveal structural domains that strongly depend on the substrate material, substrate orientation, and the film thickness. On (001) perovskite substrates of SrTiO3 and LaAlO3, the long c-axis of the orthorhombic unit cell was found always to lie in-plane parallel to one of the axes of the perovskite forming 90 degrees rotational twins with the rotation axis parallel to the [110] axis of LaFeO3 and to the substrate normal. In contrast, MgO and MgAl2O4 substrates lead to the in-plane and the out-of-plane orientation of the c-axis and give rise to smaller domains. The results are discussed with respect to the correlation between the crystallographic and the antiferromagnetic structure of LaFeO3.