  Let $(\alpha, \omega)$ be a measurable twisted action of the locally compact
group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a
differential $^*$-subalgebra of $\mathfrak B$, invariant under $(\alpha,
\omega)$. We observe that $L^1_{\alpha,\omega}({\sf G},\mathfrak A)$ is a
differential subalgebra of $L^1_{\alpha,\omega}({\sf G},\mathfrak B)$. We use
this fact to provide new examples of groups with symmetric Banach
$^*$-algebras. In particular, we prove that discrete rigidly symmetric
extensions of compact groups are symmetric or that semidirect products ${\sf
K}\rtimes{\sf H}$, with ${\sf H}$ symmetric and ${\sf K}$ compact, are
symmetric.
