The 'surfer dude' Garrett Lisi does it again. He shows the actual decomposition of the E8 group into three basic subgroups:
1.) Graviweak SO (7,1) group
2.) Strong (B-L) SO (1,7)
3.) 3 X (8 X 8) = 192 Fermions
For those of you who have been following me over the years probably remember my old website entitled, "Towards a Grand Unified Field Theory based on Phi Recursion and Quantum Gravity" where I spotlighted Garrett's original article published in ArXiv and Telegraph UK back in 2007. That original website, unbeknownst to me, is archived somewhere in cyberspace.