In the late 1970s, the Interior Ministry formed it's own Spetsnaz type units (called "Omon," or Black Berets) for hostage rescue and special raids. Not quite as good as the Spetsnaz or Spetsgruppa, the Omon still exists as sort of a super SWAT team for the national police. The Ministry of Justice has it's own Spetsgruppa, called Spetsnaz UIN (group for special assignment.) Spetsnaz UIN is used to deal with revolts or hostage situations in prisons.
There is even a private company (GROM Security Company) which employs former Spetsnaz and Spetsgruppa troopers and provides bodyguards and security services for those who can afford it. Actually, GROM is actually a semi-government organization as it's largest customer is the Russian government. By providing higher pay for Spetsnaz personnel, GROM can provide the highest level of security. The government connection insures that GROM maintains good relationships with the Spetsnaz and ministries that have Spetsgruppa.
After the Spetsnaz had been around for about ten years, various organizations in the Soviet government decided that they could use a few Spetsnaz type troops for their own special needs. Thus in the 1970s and 80s there appeared Spetsnaz clones called Spetsgruppa. The most use of these was Spetsgruppa Alfa (Special Group A), which was established in 1974 to do the same peacetime work as the U.S. Delta Force or British SAS. In other words; anti-terrorist assignments or special raids. It was Spetsgruppa Alfa that was sent to Kabul, Afghanistan, in 1980 to make sure the troublesome Afghan president Amin and his family were eliminated from the scene (killed.) Survivors (members of the presidential palace staff) of the Spetsgruppa Alfa assault reported that the Spetsnaz troopers systematically hunted down and killed their targets with a minimum of fuss. Very professional. The surviving Afghans were suitably impressed. Spetsgruppa Alfa now belongs to the FSB (successor to the KGB) and number about 300 men (and a few women.) At the same time Spetsgruppa Alfa was established, another section of the KGB organized Spetsgruppa Vympel. This group was trained to perform wartime assassination and kidnapping jobs for the KGB. The FSB also inherited Spetsgruppa Vympel, which is a little smaller than Spetsgruppa Alpha and is used mainly for hostage rescue.