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Applying the domain model to the G($2$) gauge group and the thick centervortex model to the SU($2$) and SU($3$) subgroups of G($2$), we calculate thepotentials between static sources, as well as some parameters of the vortexprofile. Comparing the results obtained from G($2$) and its subgroups, we arguethat SU($2$) and SU($3$) gauge groups have important roles in observingconfinement in the G($2$) gauge group.

Role of the SU($2$) and SU($3$) subgroups in observing confinement in the G($2$) gauge group