We study the structures of Ag adatom clusters supported on the metal Ag(111) surface using the genetic algorithm (GA). The atomic interactions are modelled by the surface-embedded-atom method. The lowest-energy structures of adatom clusters with sizes n = 3-20 are obtained, in which n = 7, 10, 12, 14, 16, 19 are the magic numbers.Furthermore, we give a series of structures with energies close to the lowest energy (the lower-energy isomers), and the structure features are studied in detail. Except for some magic clusters and small clusters, every configuration of adatom clusters generally has two distinct adsorption ways, so the isomers always appear in pairs.