  The mergers of double helium white dwarfs are believed to form isolated
helium-rich hot subdwarfs. Observation shows that the helium-rich hot subdwarfs
can be divided into two subgroups based on whether the surface is carbon-rich
or carbon-normal. But it is not clear whether this distribution directly comes
from binary evolution. We adopt the binary population synthesis (BPS) to obtain
the population of single helium-rich hot subdwarfs according to the channel of
double helium white dwarfs merger. We find that the merger channel can
represent the two subgroups in the $T_{\rm{eff}}-\log g$ plane related to
different masses of progenitor helium white dwarfs. For $Z$ = 0.02, the birth
rates and local density of helium-rich hot subdwarf stars by the mergers of two
helium white dwarfs is $\sim 4.82 \times 10^{-3}$ $\rm yr^{-1}$ and $\sim$
290.0 $\rm kpc^{-3}$ at 13.7 Gyr in our Galaxy, respectively. The proportion of
carbon-rich and carbon-normal helium-rich hot subdwarfs are 32$\%$ and 68$\%$,
respectively.
