The dogs don't have a particular rule, but they form a privileged caste on Animal Farm, only slightly below the highest level of pigs in status. They are the equivalent of a police force in a totalitarian state, and they stay close to Napoleon.
In many ways, their high status is acknowledged. For example, they sit with Napoleon, Squealer, and Minimus facing the other animals at the mandatory Sunday meetings:
Napoleon, with Squealer and another pig named Minimus, who had a remarkable gift for composing songs and poems, sat on the front of the raised platform, with the nine young dogs forming a semicircle round them, and the other pigs sitting behind. The rest of the animals sat facing them in the main body of the barn.
They personally serve and guard Napoleon:
He took his meals alone, with two dogs to wait upon him
He also has four dogs to guard his bedroom at night.
When rations are reduced, the dogs, like the pigs, are always exempt from suffering.
The dogs' main function and reason for being is to guard Napoleon and enforce his decrees by tearing apart animals who oppose him. They terrify the other animals and cause them to be afraid to complain. As the above quotes show, they are part of the ceremonial apparatus of Napoleon's dictatorship. We learn that
neither pigs nor dogs produced any food by their own labour; and there were very many of them, and their appetites were always good.
The dogs, like the pigs, are a parasitic class that perform no useful work but must be supported in comfort and style.
Because they are so well rewarded by this system of governance, they have no reason to oppose it and every reason to use their training in violence and killing to support it.