Using grazing incidence X-ray diffraction (GIXD) and density functional theory (DFT), we have studied the silicene reconstructions on Ag(111). We propose a comprehensive discussion of all nonequivalent configurations for the) 4 4 ( ,   30) 3 2 3 2 (R ,   9. 13) 13 13 (R-type I and   9. 13) 13 13 (R-type II reconstructions, putting in evidence their relative stability. We show that assuming a p3 symmetry leads to a total of 12 inequivalent reconstructions, that can be labeled according to an original notation, which specifies the occupation of the p3-symmetry Wyckoff positions by the Si atoms of the silicene unit cell and by the Ag atoms of the first three substrate layers. The DFT calculations are in good agreement with the experimental results, and report that the structures energetically most favorable are those which best reproduce the measured scanning tunneling microscopy images and the GIXD structure factors. These configurations are also those inducing the highest deformation in the substrate, suggesting that the interaction between silicene and Ag can be held to be responsible for the unexpected stability of the 2D silicon layer. 2