Clifford semigroups!

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Can someone come up with a drawing how can Clifford semigroup be presented as a decomposition of $S_{\alpha_{i}}$, where $\alpha_{i} \in E(S)$, where $E(S)$ is the set of idempotents? I've gone through a lot of books of semigroups and couldn't find something similar?

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A Clifford semigroup is a semilattice of groups. Thus take any picture representing a semilattice (Google this word and take the image tab) and replace points by groups.