  The confinement problem is studied using the thick center vortex model. It is
shown that the $SU(3)$ Cartan sub algebra of the decomposed $G(2)$ gauge theory
can play an important role in the confinement. The Casimir eigenvalues and
ratios of the $G(2)$ representations are obtained using its decomposition to
the $SU(3)$ subgroups. This leads to the conjecture that the $SU(3)$ subgroups
also can explain the $G(2)$ properties of the confinement. The thick center
vortex model for the $SU(3)$ subgroups of the $G(2)$ gauge theory is applied
without the domain modification. Instead, the presence of two $SU(3)$ vortices
with opposite fluxes due to the possibility of decomposition of the $G(2)$
Cartan sub algebra to the $SU(3)$ groups can explain the properties of the
confinement of the $G(2)$ group both at intermediate and asymptotic distances
which is studied here.
