  We prove the solvability and nilpotency of Kac--Paljutkin's finite quantum
group and Sekine quantum groups and we classify the solvable series of
Kac--Paljutkin's finite quantum group via Cohen--Westreich's Burnside theorem.
Some semisimple quasitriangular Hopf algebras of dimensions $2pq$ are also
studied. In Appendix A, we give a direct computation of the universal
$R$-matrices for Kac--Paljutkin's $8$-dimensional finite quantum group.
