We present an analysis of the spatial orientations of 323 galaxies in the cluster Abell 3558. Our aim is to examine non-random effects in galaxy orientations in the subsample of the cluster. The ``position angle-inclination'' method is used to find the three-dimensional rotation axes. To check for anisotropy or isotropy we carried out three statistical tests: Fourier, Kolmogorov-Smirnov, and Kuiper-V. We assumed a spatially isotropic distribution to examine non-random effects. The galaxies found in the investigated cluster region show isotropy in both two- and three-dimensional analyses of the galactic coordinate system. In addition, it is found that the overall isotropic appearance cannot be maintained when looking at the subsamples. The low radial-velocity galaxies in A3558 showed anisotropy in both two- and three-dimensional analyses. A weak anisotropy is noticed in the hard X-ray emission region. Few subsamples shows similar alignments with respect to both the galactic and Supergalactic coordinate systems. We offer possible explanations of these anisotropies.