Debian/Ubuntu:

apt install --no-install-recommends sssd-tools libnss-sss libpam-sss

/etc/sssd/sssd.conf

[sssd]
services = nss,pam
config_file_version = 2
domains = LOCAL
 
[domain/LOCAL]
id_provider = local

chmod 600 /etc/sssd/sssd.conf

sssctl config-check
service sssd restart

sss_useradd testuser1
sss_useradd testuser2

sss_groupadd testgroup1
sss_groupadd testgroup2

sss_usermod -a testgroup1 testuser1
sss_usermod -a testgroup2 testuser2

sss_groupshow testgroup1
sss_groupshow testgroup2
getent group testgroup1
getent group testgroup2

sss_groupmod -a testgroup2 testgroup1

sss_groupshow testgroup1
sss_groupshow testgroup2
getent group testgroup1
getent group testgroup2