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In this paper we study the problem of classification of indecomposablesolutions of the Yang-Baxter equation. Using a scheme proposed by Bachiller,Ced\'o, and Jespers, and recent advances in the classification of braces weclassify all indecomposable solutions with some particular permutation groups.We do this for all groups of size $pq$, all abelian groups of size $p^2q$ andall dihedral groups of size $p^2q$.

Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes $pq$ and $p^2q$