Not much is known about the Quyth Government but one can make several assumptions based on the social structure of their species. It is more than likely that the Quyth Leaders are in charge in some form. On many levels it appears that much of the Concordia is run by Organized Crime as many of the major organizations and businesses are run by those connected to mob activity.
As one of the few governments in the known galaxy who are not controlled by the Creterakian empire the Quyth have developed a "Freedom isn't free" philosophy. During the Creterakian take over of the Galaxy the Quyth were known to kill hundreds of thousands of Quyth to ensure The Creterakians would not gain a a foothold on their planets and space stations. This form of honor has become especially important to Quyth Warriors
The first mention of the Quyth on the Galactic stage is in 2552 when they achieved Faster than Light capability (FTL) at the end of the Second Galactic War. As the last of the major galactic species to achieve FTL Travel, many discounted the Quyth as a minor player on the galaxy. This seems much at odds with one of the few independent species left in the Galaxy.
It would be in the year 2572 that a glimmer of the Quyth strength would be seen when the Quyth attack the planet Reiger with a 400 ship armada crushing all opposition and enslaving the planet's population. The Quyth would strike again in that same year capturing the planet Gritchlik from the Sklorno empire. Before the end of the year the Quyth would have to defend their newly conquered holdings; while holding off the Planetary Union on Reiger, the Sklorno managed to saturation bomb Gritchlik as they left the planet.
Ironically it was this action by the Sklorno which thrust the Quyth from secondary galaxy player to galactic front runner. In the year 2573 the Quyth shocked the galaxy by not only establishing a permanent colony on Gritchlik, But also on Whitok which had been saturation bombed in 2524 as well as Chikchik, and Ionath, saturation bombed in 2558. The Quyth displayed an unforeseen ability to not only survive but thrive in irradiated environments.
It was this ability to survive which allowed the Quyth to fight off the Creterakian take over of most of the known galaxy. As the Creterakian war strategy involved bypassing standing navies to land overwhelming numbers on the surface of individual planets, the Quyth irradiated worlds eliminated this Creterakian Advantage as the Creterakians could not survive in the radiation-filled environments. This left the Quyth to defend their homeworld with all remaining resources including all three of the mobile but indomitable space stations. Faced by millions of Quyth, and the incomparable industrial capacity of the trio of Quyth space stations The Creterakians abandoned efforts to try and pacify the Concordia in 2642.