  We study $N=2$ seven-dimensional gauged supergravity coupled to three vector
multiplets with $SO(4)$ gauge group. The resulting gauged supergravity contains
10 scalars consisting of the dilaton and 9 vector multiplet scalars
parametrized by $SO(3,3)/SO(3)\times SO(3)$ coset manifold. The maximally
supersymmetric $AdS_7$ vacuum with unbroken $SO(4)$ symmetry is identified with
a $(1,0)$ SCFT in six dimensions. We find one new supersymmetric $AdS_7$
critical point preserving $SO(3)_{\textrm{diag}}\subset SO(3)\times SO(3)\sim
SO(4)$ and study a holographic RG flow interpolating between the $SO(4)$ and
the new $SO(3)$ supersymmetric critical points. The RG flow is driven by a
vacuum expectation value of a dimension-four operator and describes a
deformation of the UV $(1,0)$ SCFT to another supersymmetric fixed point in the
IR. In addition, a number of non-supersymmetric critical points are identified,
and some of them are stable with all scalar masses above the BF bound. RG flows
to non-conformal $N=(1,0)$ Super Yang-Mills with $SO(2)\times SO(2)$ and
$SO(2)$ symmetries are also investigated. Some of these flows have physically
acceptable IR singularities since the scalar potential is bounded above. These
provide physical RG flows from $(1,0)$ SCFT to non-conformal field theories in
six dimensions.
