It depends; there are hunting dogs and more.
A pit bull is classified in the terrier group in the AKC, its a working dog, and it is in the Molosser family.
Grasshoppers can be classified into the insects group.
Yes. According to the American Kennel Club, all Setters are classified in the Sporting group.
Non-Sporting Group
What height and weight should a dog be to be classified large
Shih Tzu's are classified in the Toy Breed group.
Kingdom: Dog You
Canine
They are in the Working group, and they are classified as Sled Dogs.
dog
Dogs are classified as mammals.
They are classified as Bivalves, however that is just the class