  This paper studies the multiplicity of normalized solutions to the
Schr\"{o}dinger equation with mixed nonlinearities \begin{equation*}
\begin{cases} -\Delta u=\lambda u+h(\epsilon x)|u|^{q-2}u+\eta |u|^{p-2}u,\quad
x\in \mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=a^2, \end{cases}
\end{equation*} where $a, \epsilon, \eta>0$, $q$ is $L^2$-subcritical, $p$ is
$L^2$-supercritical, $\lambda\in \mathbb{R}$ is an unknown parameter that
appears as a Lagrange multiplier, $h$ is a positive and continuous function. It
is proved that the numbers of normalized solutions are at least the numbers of
global maximum points of $h$ when $\epsilon$ is small enough. Moreover, the
orbital stability of the solutions obtained is analyzed as well. In particular,
our results cover the Sobolev critical case $p=2N/(N-2)$.
