Which taxonomic rank is the next-smallest after Order?

Answer 1

From largest to most specific, the order is  Domain, Kingdom, Phylum, Class, Order, Family, Genus, species.

The nest smallest after Order is Family.

Answer 2

The next smallest taxonomic rank after order is family.

Answer 3

The next level is Family. The levels, from most to least inclusive, are Kingdom, Phylum, Class, Order, Family, Genus, and Species.