  We provide a second order energy expansion for a gas of $N$ bosonic particles
with three-body interactions in the Gross-Pitaevskii regime. We especially
confirm a conjecture by Nam, Ricaud and Triay in [21], where they predict the
subleading term in the asymptotic expansion of the ground state energy to be of
the order $\sqrt{N}$. In addition, we show that the ground state satisfies
Bose-Einstein condensation with a rate of the order $\frac{1}{\sqrt{N}}$.
