  Let $k$ be a field of characteristic not equal to $2,3$, $\mathbb{O}$ an
octonion over $k$ and $\mathcal{J}$ the exceptional Jordan algebra defined by
$\mathbb{O}$. We consider the prehomogeneous vector space $(G,V)$ where
$G=GE_6\times \mathrm{GL}(2)$ and $V=\mathcal{J}\oplus \mathcal{J}$. We prove
that generic rational orbits of this prehomogeneous vector space are in
bijective correspondence with $k$-isomorphism classes of pairs
$(\mathcal{M},\mathfrak{n})$ where $\mathcal{M}$'s are isotopes of
$\mathcal{J}$ and $\mathfrak{n}$'s are cubic \'etale subalgebras of
$\mathcal{M}$. Also we prove that if $\mathbb{O}$ is split, then generic
rational orbits are in bijective correspondence with isomorphism classes of
separable extensions of $k$ of degrees up to $3$.
