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In this letter we present a new perspective for the study of the Public Goods games on complex networks. The idea of our approach is to consider a realistic structure for the groups in which Public Goods games are played. Instead of assuming that the social network of contacts self-defines a group structure with identical topological properties, we disentangle these two interaction patterns so to deal with systems having groups of definite sizes embedded in social networks with a tunable degree of heterogeneity. Surpisingly, this realistic framework, reveals that social heterogeneity may not foster cooperation depending on the game setting and the updating rule.