  We study supersymmetric solutions in four-dimensional $N=6$ gauged
supergravity with $SO(6)$ gauge group. There is a unique $N=6$ supersymmetric
$AdS_4$ vacuum with $SO(6)$ symmetry dual to an $N=6$ SCFT in three dimensions.
We find a number of domain walls interpolating between this $AdS_4$ vacuum and
singular geometries in the IR with $SO(2)\times SO(4)$, $U(3)$, $SO(3)$ and
$SO(2)\times SO(2)\times SO(2)$ symmetries. The $SO(3)$ case admits $N=6$ or
$N=2$ solutions depending on whether the pseudoscalars are present or not. On
the other hand, all the remaining solutions preserve $N=6$ supersymmetry. These
solutions describe RG flows from the $N=6$ SCFT to non-conformal field theories
driven by mass deformations. In particular, the $SO(2)\times SO(4)$ solution is
in agreement with the previously known mass deformations of the dual $N=6$
SCFT. We also give a supersymmetric Janus solution with $SO(2)\times SO(4)$
symmetry, describing two-dimensional conformal defects in the $N=6$ SCFT with
unbroken $N=(4,2)$ supersymmetry. Finally, we find an $N=2$ supersymmetric
$AdS_2\times H^2$ solution with $SO(2)\times SO(4)$ symmetry and the
corresponding domain wall interpolating between this fixed point and the
$AdS_4$ vacuum. The solution describes an $AdS_4$ black hole with a magnetic
charge and is dual to a twisted compactification of the $N=6$ SCFT on a
hyperbolic space $H^2$. We also give a domain wall interpolating between a
locally supersymmetric $AdS_4$ and a curved domain wall with $SO(2)\times
SO(2)\times SO(2)$ symmetry dual to an RG flow across dimensions from the $N=6$
SCFT to a supersymmetric quantum mechanics.
