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Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12)and G2 (at levels 3,4) can be obtained from conformal embeddings. We determinethe associated alge bras of quantum symmetries and discover or recover, as aby-product, the graphs describing exceptional quantum subgroups of type B2 orG2 which encode their module structure over the associated fusion category.Global dimensions are given.

Exceptional quantum subgroups for the rank two Lie algebras B2 and G2