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We continue the study undertaken in \cite{DV} of the exceptional Jordanalgebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in analmost classical space-time approach to particle physics. Along with reviewingknown properties of $J$ and of the associated exceptional Lie groups we arguethat the symmetry of the model can be deduced from the Borel-de Siebenthaltheory of maximal connected subgroups of simple compact Lie groups.

Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra