  In this paper, we study the semilinear subelliptic equation \[ \left\{
  \begin{array}{cc}
  -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~\Omega, \\[2mm]
  u=0\hfill & \mbox{on}~\partial\Omega,
  \end{array}
  \right. \] where $\triangle_{X}=-\sum_{i=1}^{m}X_{i}^{*}X_{i}$ is the
self-adjoint H\"{o}rmander operator associated with vector fields
$X=(X_{1},X_{2},\ldots,X_{m})$ satisfying the H\"{o}rmander condition,
$f(x,u)\in C(\overline{\Omega}\times \mathbb{R})$, $g(x,u)$ is a
Carath\'{e}odory function on $\Omega\times \mathbb{R}$, and $\Omega$ is an open
bounded domain in $\mathbb{R}^n$ with smooth boundary. Combining the
perturbation from symmetry method with the approaches involving eigenvalue
estimate and Morse index in estimating the min-max values, we obtain two kinds
of existence results for multiple weak solutions to the problem above.
Furthermore, we discuss the difference between the eigenvalue estimate approach
and the Morse index approach in degenerate situations. Compared with the
classical elliptic cases, both approaches here have their own strengths in the
degenerate cases. This new phenomenon implies the results in general degenerate
cases would be quite different from the situations in classical elliptic cases.
