- You may be looking for the Cardassian Union, the prime-universe Cardassian government, or the Cardassian home planet, Cardassia Prime.
The Cardassian Theonomy is the formal name of an alternate-universe Cardassian government; this interstellar territory, whose capitol is on Cardassia Prime, is most commonly referred to as the worlds of Cardassia or simply as Cardassia. It is the direct successor of the First Hebitian society, carrying on its traditions in a reformed manner.
This government in its current form was established in the nineteenth century (by Earth reckoning), in the beginning of the Cataclysm. It encompasses the worlds of the Cardassia system itself, a number of colonies, and several other worlds more recently settled and farmed or mined, as the case may be, to support the ailing world of Cardassia Prime; these worlds were all uninhabited, prior to Cardassian settlement. The Theonomy also has diplomatic and trade relations with a number of neighboring powers. It has had border disputes with the Klingon Empire.
One of these neighboring powers, however, had aggressive designs on the Cardassian Theonomy. Bajoran forces invaded Cardassia in 2325, leading to an occupation that was still going as of 2370 despite attacks by the Cardassian Resistance. The Bajorans saw themselves, and their deities, the Pah-Wraiths, as having a religious duty to convert the Oralian believers or destroy them if they would not yield. (Star Trek: Sigils and Unions--"The Desolate Vigil")
The United Federation of Planets refused Cardassian pleas for help during the onset of the invasion on Prime Directive grounds, claiming that the presence of religious motivations meant they could not interfere. That did not stop some Federation civilians from acting on a small scale to help the Cardassian plight, to include the adoption of some Cardassian children to raise them away from the horrors of the Occupation. (Star Trek: Sigils and Unions--"The Exile," "The Image and the Spirit")
The Cardassian Theonomy, while not a wholly secular government, is generally democratic in its workings. Both religious and secular powers are represented in its government, and one of its fundamental legal guarantees is the Right of Worship, which grants religious freedom to all who are born of Cardassian blood or who live legally in Cardassian territory. The name itself represents something of a compromise: "Cardassian" is a secular term for its people (as opposed to the religiously-charged term "Hebitian," which means "people with souls"), whereas "Theonomy" implies that its laws are based on absolute moral principles ordained by Oralius. That said, it has been stated by some Cardassians, such as Hirhul Mendral, that while Cardassian laws and social mores are generally conservative, more is allowed under the codified law than most Oralian clerics would condone. (Sigils and Unions: Catacombs of Oralius--"The Desolate Vigil," "The Image and the Spirit")