This is the complete list of genera belonging to the family Apiaceae, as per the Germplasm Resources Information Network. This listing contains 454 genera, and is divided up into sub-taxons.
Subfamily Apioideae
The NCBI Taxonomy Browser lists the Tribes Saniculeae and Steganotaenieae in a separate subfamily, Saniculoideae.
References
List of Apiaceae genera Wikipedia(Text) CC BY-SA