Maximal subgraph mining is increasingly important in various domains, including bioinformatics, genomics, and chemistry, as it helps identify common characteristics among a set of graphs and enables their classification into different categories. Existing approaches for identifying maximal subgraphs typically rely on traversing a graph lattice. However, in practice, these approaches are limited to relatively small subgraphs due to the exponential growth of the search space and the NP-completeness of the underlying subgraph isomorphism test. In this work, we propose SCAMA, an approach that addresses these limitations by adopting a divide-and-conquer strategy for efficient mining of maximal subgraphs. Our approach involves initially partitioning a graph database into equivalence classes using bootstrapped backbones, which are tree-shaped frequent subgraphs. We then introduce a learning process based on a novel graph convolutional network (GCN) to extract maximal backbones for each equivalence class. A critical insight of our approach is that by estimating each maximal backbone directly in the embedding space, we can avoid the exponential traversal of the graph lattice. From the extracted maximal backbones, we construct the maximal frequent subgraphs. Furthermore, we outline how SCAMA can be extended to perform top-k largest frequent subgraph mining and how the discovered patterns facilitate graph classification. Our experimental results demonstrate the effectiveness of SCAMA in identifying almost perfectly maximal frequent subgraphs, while exhibiting approximately 10 times faster performance compared to the best baseline technique.