To try to understand the deformation of $p$-divisible group more explicit, I am thinking given a connected $p$-divisible group $G_0$ on $\overline{\mathbb{F}_q}$, Choose a deformation $G$ of $G_0$ over $W(\overline{\mathbb{F}_q})/p^2$, then it determines a filtration in Dieudonné module (maybe up to $p^2$?). If that is the case, how can we describe $G[p]$ over $W(\overline{\mathbb{F}_q})/p^2$ in terms of this filtration in its Dieudonné module?

Also please point out if I misunderstood something.