What is the relationship between kingdom and species in terms of size and number of groups in each?

Directly proportional
As kingdom grows the more species are in the classifying group. 
And since there are only a number of kingdom and thousand species, it would account that species changes more rapidly and exponentially grows than kingdoms.

A. FAMILY, GENUS, SPECIES, SUBSPECIES.

The complete and correct hierarchy of taxonomic groups from largest to smallest are:
1) Domain
     1.1) Archaea  1.2) Bactera  1.3) Eukarya
2) Kingdom
     2.1) Animalia  2.2) Plantae  2.3) Fungi  2.4) Protista  2.5) Archaea  2.6) Bacteria
3) Phylum - has 35 phyla
4) Class 
5) Order
6) Family
7) Genus
8) Species