Traditional classification of organisms is organized like this (from the largest, most generic groupings to the smallest, most specific groupings of organisms):
Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species
Canines come from the genus Canis. Felines come from the genus Felis. The root word Herp includes reptiles as well as amphibians.
Fish are fairly complicated as there is no specific genus that includes all fish. You really have be at the class level to include all fish. The three MAIN classes of fish extant (not extinct) today are:
Agnatha (jawless fish), Chondrichthyes (cartilaginous fish, including sharks), and Osteichthyes (trout, salmon, etc.)
However the most common root (of Latin origin) that refers to fish as a whole is piscine.
So in the spirit of what you're asking the answer is PISCINE.
*NOTE: you should see that bony and cartilaginous fishes both share the Greek root "ichthy" which also refers to all fish as whole.
Daeids or something?