  The recent discovery of a charge density wave order at the wave vector $P$
$(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ in the kagome metal ScV$_6$Sn$_6$ has
created a mystery because subsequent theoretical and experimental studies show
a dominant phonon instability instead at another wave vector $H$
$(\frac{1}{3},\frac{1}{3},\frac{1}{2})$. In this paper, I use first principles
total energy calculations to map out the landscape of the structural
distortions due to the unstable phonon modes at $H$, $L$
$(\frac{1}{2},0,\frac{1}{2})$, and $P$ present in this material. In agreement
with previous results, I find that the distortions due to the $H$ instability
cause the largest gain in energy relative to the parent structure, followed in
order by the $L$ and $P$ instabilities. However, only two distinct structure
occur due to this instability, which are separated by 6 meV/f.u. The
instability at $L$ results in three distinct structures separated in energy by
5 meV/f.u. In contrast, six different distorted structures are stabilized due
to the instability at $P$, and they all lie within 2 meV/f.u.\ of each other.
Hence, despite a lower energy gain, the condensation at $P$ could be favorable
due to a larger entropy gain associated with the fluctuations within a manifold
with larger multiplicity via the order-by-disorder mechanism.
