The impact of amorphous phases around the holes and at the upper and lower free surfaces on thermal transport in silicon phononic membranes is studied. By means of molecular dynamics and Monte Carlo simulations, we explore the impact of the amorphous phase (oxidation and amorphous silicon), surfaces roughness, and a series of geometric parameters on thermal transport. We show that the crystalline phase drives the phenomena; the two main parameters are (i) the crystalline fraction between two holes and (ii) the crystalline thickness of the membranes. We reveal the hierarchical impact of nanostructurations on the thermal conductivity, namely, from the most resistive to the less resistive: the creation of holes, the amorphous phase around them, and the amorphization of the membranes edges. The surfaces or interfaces perpendicular to the heat flow hinder the thermal conductivity to a much greater extent than those parallel to the heat flow.