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