The taxonomy of the Asilidae have been somewhat revised by Torsten Dikow as of July 2009. Here is a cladogram showing the latest thought on relationships within this group:
Summary of relationships of subfamily taxa based on strict consensus topology (Dikow 2009a, Fig. 120). Character state optimization and distribution for higher-level clades mapped onto cladogram with character number above circle and character state below circle; green circle = autapomorphy; yellow circle = apomorphic character states (reversed or homoplasious somewhere else in the tree).
Here is a link to the original reference by Torsten Dikow, who kindly gave me permission to use this cladogram.