Define $Stab^{+}(\Omega )$={ $\phi \in GL^{+}(V)$ : $\phi^{*}\Omega=\Omega$ }.

we say three-form $\Omega\in\wedge^{3}V^{*}$ is non-degenerate , if $i_X\Omega\neq 0$ for all $X\in V$-{0}

Let $V\cong \mathbb{R}^{6}$ and $\Omega\in\wedge^{3}V^{*}$ be non-degenerate(by sense of Hitchin) . Then we know $Stab^{+}(\Omega )=SL(3,\mathbb{R})\times SL(3,\mathbb{R})$ OR $Stab^{+}(\Omega )=SL(3,\mathbb{C}))$

We call the three-form $\Omega\in\wedge^{3}V^{*}$ is n-fold degenerate if the annihilator of $\Omega$, i.e.,

$Ann(\Omega)$={ $X\in V$ : $ i_X\Omega=0$ } has $dim(Ann(\Omega)=n$ so my question is what can we say about $Stab^{+}(\Omega )$ when $\Omega$ is n-fold degenerate?( $n$ here is 0,1,3,or 6)