Mellipedes fall under the following class of Arthropoda

Mellipedes fall under the Myriapoda class of Arthropoda.
Millipedes are a group of arthropods that are characterized by having two pairs of jointed legs on most body segments, and class Diplopoda. Diplopoda is the largest class of myriapods, an arthropod group that also includes centipedes and other multi-legged creatures.
Among myriapods, millipedes have traditionally been considered most closely related to the tiny pauropods, although some molecular studies challenge this relationship.