Groups　play　a　crucial　role　in　decision-making　of　social　networks,　since　individual　decision-making　is　often　influenced　by　groups.　This　brings　the　Group　Influence　Maximization　(GIM)　problem　which　aims　to　maximize　the　expected　number　of　activated　groups　by　finding　k　seed　nodes.　The　GIM　problem　has　been　proved　NP-hard　while　computing　the　objective　function　is　#　P　-hard　under　Independent　Cascade　(IC)　model.　We　propose　an　algorithm　called　Maximizing　Group　Coverage　(MGC)　which　greedily　selects　the　best　node　based　on　evaluating　the　contribution　of　nodes　to　the　groups,　ensuring　the　success　of　approximating　the　maximization　of　the　number　of　activated　groups.　Finally,　we　compare　the　MGC　algorithm　with　the　baseline　algorithm　called　Maximum　Coverage　(MC)　through　experiments,　demonstrating　that　MGC　outperforms　MC　under　IC　model　regarding　the　average　number　of　activated　groups.　©　2021,　Springer　Nature　Switzerland　AG.