We numerically study structural properties of mechanically stable packings of hard spheres (HS), in a wide range of packing fractions 0.53 <=phi <= 0.72. Detailed structural information is obtained from the analysis of orientational order parameters, which clearly reveals a disorderorder phase transition at the random close packing (RCP) density, phi(c) similar or equal to? 0.64. Above phi(c), the crystalline nuclei form 3D-like clusters, which upon further desification transform into alternating planar-like layers. We also find that particles with icosahedral symmetry survive only in a narrow density range in the vicinity of the RCP transition.