Final answer:
Cats and dogs are considered part of the same group at the Order level, specifically the Order Carnivora, in the taxonomic classification system.
Step-by-step explanation:
The taxonomic classification system allows us to group organisms based on shared characteristics. In the case of cats and dogs, they are first considered part of the same group at the Order level. Cats are members of the family Felidae, while dogs belong to the family Canidae, but both share the Order Carnivora, which is where they are grouped together. Beyond the Order level, they diverge into different families and hence are no longer in the same group.