Terrier Group is the name of a breed Group of dogs, used by kennel clubs to classify a defined collection of dog breeds. In general, a Terrier Group includes one particular type of dog, the Terrier, although other types may be included in a kennel club's Terrier Group.Most major English-language kennel clubs include a Terrier Group although different kennel clubs may not include the same breeds in their Terrier Group.hen the classifications were changed, the dogs within the Jack Russell Terrier breed that were over 12 tall at the withers were moved into the Parson Russell Terrier breed. Any dog in the Jack Russell Terrier breed at this time (within the UKC) may not be over 12 tall.