From SuspireWiki

While the Ordo Dracul is traditionally set up such that only Dracula himself has total control over the covenant, in his absence the Sworn of the Dragon rule. They hold tremendous status in the covenant (mechanically, only Sworn may have an Ordo Dracul status of 4 or 5). The Sworn are divided into three branches, described below; each has its own purpose, and may not subvert the authority of the other branches.

Please note that on the suspire.org server it is not possible to enter the game as a member of the Sworn (i.e., it must be earned in character through Coil progressions and tests). Furthermore, a character must be at least a Scholar to test.

The Sworn of the Axe

The Sworn of the Axe rule all that is martial in the Ordo Dracul. They may declare what are effectively covenant bloodhunts on individuals, and are charged in times of war with managing the Academy (it's not unheard of for the Axe to declare a war and maintain it in order to seize power from the Sworn of Mysteries). Many Guardians hail from these Sworn. They are said to have been founded by Mara, and their color is red, for fire and blood.

The Sworn of the Dying Light

The Dying Light manage all academic affairs in the covenant, and therefore their power is considerable in this highly studious society. They may set the Academy, individually or as a body, to certain reseach tasks, and may set others off-limits. It is necessary to have at least one Dying Light on a Juris Draconis for it to be considered binding by the Ordo Dracul. The Dying Light was founded by Anoushka, and their color is the deep indigo-blue of the rising and setting sun.

The Sworn of Mysteries

The Mysteries manage all things political, and may set the course thereby for the entire covenant--although Ordo Dracul law renders them incapable of passing judgment on individuals. As can be imagined, the Mystery-Sworn often bicker (and sometimes more than bicker) with the Axe-Sworn on policy matters. These Sworn are tightly bound by symbols and titles that are esoteric and obscure, even for Dragons... The Sworn of Mysteries was founded by Lizette, and their color is black or sable, for a darkness waiting to be pierced by illumination.

It is advisable to read the Ordo Dracul book for full information on the Sworn. The above is just a summary.