The asymmetric unit of the title compound, [Ag(C(5)H(8)N(4))(3)](CF(3)O(3)S)·C(5)H(8)N(4), contains two cations, two anions and two uncoordinated 3-amino-5,6-dimethyl-1,2,4-triazine (admt) ligands. It was prepared from the reaction of silver trifluoro-methane-sulfonate and admt in a 2:3 molar ratio. Both silver(I) ions are bonded to three admt mol-ecules via their 2-position triazine N atoms in almost regular trigonal-planar geometries. Three intra-molecular N-H⋯N hydrogen bonds between adjacent admt mol-ecules in each cation help to maintain their overall near planarities (r.m.s. deviations for the 28 non-H atoms = 0.139 and 0.153 Å). In the crystal, numerous N-H⋯N, N-H⋯O, C-H⋯O, C-H⋯N and C-H⋯F hydrogen-bonding interactions link the components into a three-dimensional network.