  Both observations and cosmological simulations have recently shown that there
is a large scatter in the number of satellites of Milky Way (MW)-like galaxies.
In this study, we investigate the relation between the satellite number and
galaxy group assembly history, using the $r-$band magnitude gap ($\Delta
m_{12}$) between the first and the second brightest galaxy as an indicator.
From 20 deg$^2$ of Hyper Suprime-Cam Subaru Strategic Program Wide layer, we
identify 17 dwarf satellite candidates around NGC 4437, a spiral galaxy with
about one-fourth of the MW stellar mass. We estimate their distances using the
surface brightness fluctuation (SBF) method. Then we confirm five candidates as
members of the NGC 4437 group, resulting in a total of seven group members.
Combining the NGC 4437 group (with $\Delta m_{12} = 2.5$ mag) with other groups
in the literature, we find a stratification of the satellite number by $\Delta
m_{12}$ for a given host stellar mass. The satellite number for given host
stellar mass decreases as $\Delta m_{12}$ increases. The same trend is found in
simulated galaxy groups in IllustrisTNG50 simulations. We also find that the
host galaxies in groups with a smaller $\Delta m_{12}$ (like NGC 4437) have
assembled their halo mass more recently than those in larger gap groups, and
that their stellar-to-halo mass ratios (SHMRs) increase as $\Delta m_{12}$
increases. These results show that the large scatter in the satellite number is
consistent with a large range of $\Delta m_{12}$, indicating diverse group
assembly histories.
