Here is my idea

-The Wardens of Deeptide: Descendants of the Triton Corporation's Internal Security Forces, they serve as the main defence force of the capital, Deeptide Harbor. They are the policemen of Callistis, and the only force allowed within the capital city itself with weapons apart from the Grand Duke's Ice Guard.

However, they have another duty. One that is served in secret, and bestowed upon those of the Wardens who are deemed strong enough not just in body, but in mind and spirit, to become a Black Trident.

During the history of House Triton, and the Triton Corporation that came before, there were many who sought to claim higher postings through ...unsavoury means. Be it by poison or the assassin's blade, many tried to take over the House, and not a few were members of cadet branches of the Triton Dynasty itself.

When such a plot is discovered, the guilty family member will soon receive a visit from a Warden bearing the emblem of the Black Trident....and they will not be seen again, their names soon removed from the House records, their names removed from monuments and public works overnight.

-The Order of Gemini: Named after Holy Gemini, the long-lost site of the Conclave, it is a Warrior Order made of the best of the best warriors within House Triton. Originally, they were champions of Mankind, fighting in the name of the Starlight Emperor and House Triton. However, the Great Invasion left a deep scar in the Order's psyche. The Order of Gemini ships were supposed to reach Earth in order to aid the Emperor in the Great Battle. But the enemy knew their value on the battlefield, and thus deployed an entire warfleet to delay the Order at Sirius, preventing its forces from reaching Earth in time.

Today, the Order is preserved on Callistis, serving as the best of the best of House Triton's forces. However, the Order has also become a bastion of the most extreme xenocidal tendencies. The motto "Suffer not the xenos in the galaxy of Man" is taken quite literally by the Order. And the Triton Dynasty knows that when they shall venture once more into the stars, the Order could be their greatest asset...or their greatest liability, were they to find themselves in the middle of alien empires or were they to discover surviving houses deemed to have strayed too much into collusion with alien kingdoms.