toothy cows scientific classification

Okay so some scientific terms and explanations first, The classification of animals goes, domain, kingdom, phylum, class, order, family, genus, species. Our discussion starts with class mamilla, so mammals. we will be focusing on order Artiodactyla, (which consist of plant eating, even toed animals, (there are other conditions)) and order Carnivora, (carnivores). So this is where Toothy cows come in, they don't fit in Artiodactyla, since they're carnivores, so they wont be categorized with regular cows. So they would be in order Carnivora, since they're carnivores. So then we get to the suborders of Carnivora, which basically amount to cats and dogs. So my question is, are Toothy cows cats or dogs. (note: i did research for this, my platform was google... (not the most reliable...))

In simple terms: we have mammals, Toothy cows have fur, they eat meat so they're carnivores, and the carnivores are divided into different families (about 12 if I'm correct), however those fall into the streamlining of cats or dogs (suborders Feliformia and Califormia)

So how does this work? What are toothy cows?