The Group D_{2} (edge) 

Silviu Radu did most of the analysis of the 98304 different cubes of this subgroup. Here the the table with the distances, the average distance is 16.93:
Up to Msymmetry there are 23232 cubes which exactly have this symmetry.
All cubes can be solved within 20 moves and there are 12 cubes up to Msymmetry
which need 20 moves. All except 2 of these cubes are antisymmetric (that
is the inverse is Msymmetric to the cube itself).
If you are interested in a list of all optimal maneuvers for this subgroup, they are included in the file D2e.zip. The 11 20f*maneuvers up to Msymmetry and Mantisymmetry are also included in the file 20moves.zip.


Cube display with AnimCubeJS 

© 2017 Herbert Kociemba 