  We study properties of the $^{12}$C nucleus within the generalized Skyrme
model where, in addition to the standard massive Skyrme model, the sextic term
and the pionic potential squared are included. We find that the model continues
to accurately describe the rotational bands of the $^{12}$C nucleus. In
addition, at variance with the case of the standard Skyrme model, it provides
the correct energy ordering of the classical solutions which correspond to the
ground state and the Hoyle state, respectively.
