  Recently, Bostan and his coauthors investigated lattice walks restricted to
the non-negative octant $\mathbb{N}^3$. For the $35548$ non-trivial models with
at most six steps, they found that many models associated to a group of order
at least $200$ and conjectured these groups were in fact infinite groups. In
this paper, we first confirm these conjectures and then consider the
non-$D$-finite property of the generating function for some of these models.
