  Let $C_n$, $Q_n$ and $D_n$ be the cyclic group, the quaternion group and the
dihedral group of order $n$, respectively. The structures of the unit groups of
the finite group algebras $FQ_{12}$ and $F(C_2 \times Q_{12})$ over a finite
field $F$ have been studied in J. Gildea, F. Monaghan (2011), F. Monaghan
(2012), G. Tang, Y. Gao (2011) and G. Tang, Y. Wei, Y. Li (2014) whereas the
structures of the unit groups of the finite group algebras $FD_{12}$ and $F(C_2
\times D_{12})$ have been studied in J. Gildea, F. Monaghan (2011), N.
Makhijani, R. K. Sharma, J. B. Srivastava (2016), F. Monaghan (2012), M. Sahai,
S. F. Ansari and G. Tang, Y. Gao (2011). In this paper, we continue this study
and establish the structures of the unit groups of the group algebras $F(C_n
\times Q_{12})$ and $F(C_n \times D_{12})$, over a finite field $F$ of
characteristic $p$ containing $p^k$ elements.
