We define and study a family of partitions of the wonderful compactification \bar{ G} of a semi-simple algebraic group G of adjoint type. The partitions are obtained from subgroups of G \times G associated to triples (A_1, A_2, a), where A_1 and A_2 are subgraphs of the Dynkin graph \Gamma of G and a : A_1 \to A_2 is an isomorphism. The partitions of \bar{ G} of Springer and Lusztig correspond respectively to the triples (\emptyset, \emptyset, \id) and (\Gamma, \Gamma, \id).
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