The practice of lobbying in the interest of economic or social groups plays an important role in the policy making process of most economies. We carry out a multi-level network analysis of the relations among lobbying organizations in the EU transparency register, focusing on the domain of finance and climate. We find that the network centrality of organizations has no simple relation with their size and each layer provides additional complementary information to characterize organizations' influence. At a more aggregate level, groups of interest differ very much in terms of internal cohesiveness and thus in their ability to advocate coherently. Groups also differ in their centrality and thus in their ability to influence each other.