Let $G$ be a compact Lie group which acts by symplectomorphisms on a symplectic manifold $(M,\omega)$. Futhermore let $\mu \colon M \to \mathfrak g$ be a moment map for this action. Denote by $\Omega = \mu^{-1}(0)$ and $M_{\rm red}$ the reduced space $\Omega/G$ (we do not assume that $0$ is a regular value). It is known that $G$ has a principal orbit $M_{(H)}$ in $M$ which is open and dense. Let $(H)$ be its orbit type for $H$ a closed subgroup of $G$.

On the other side following Theorem 5.9 (together with Remark 5.10) of Sjamaar and Lerman every connected component of $M_{\rm red}$ has a unique open and dense piece $(M_{red})_{(\tilde H)} = (M_{(\tilde H)} \cap \Omega)/G$ for $\tilde H$ another closed subgroup of $G$.

Question: Are $(H)$ and $(\tilde H)$ of the same orbit type? If not is there an example such that $(H)\neq (\tilde H)$?