  We consider maximal gauged supergravity in 4D with ISO(7) gauge group, which
arises from a consistent truncation of massive IIA supergravity on a
six-sphere. Within its G$_2$ invariant sector, the theory is known to possess a
supersymmetric AdS extremum as well as two non-supersymmetric ones. In this
context we provide a first order formulation of the theory by making use of the
Hamilton-Jacobi (HJ) formalism. This allows us to derive a positive energy
theorem for both non-supersymmetric extrema. Subsequently, we also find novel
non-supersymmetric domain walls (DW) interpolating between the supersymmetric
extremum and each of the other two. Finally, we discuss a perturbative HJ
technique that may be used in order to solve for curved DW geometries.
