  We consider simple loopless finite undirected graphs. Such a graph is called
strongly regular with parameter set (v,k,l,m), for short a srg(v,k,l,m), iff it
has exactly v vertices, each of them has exactly k neighbours, and the number
of common neighbours of any two different vertices is l if they are neighbours
and m otherwise.
  The G2(4) graph is a well-known srg(416,100,36,20). In this article, we
explicitly construct it and a certain subgraph E induced by 320 vertices in the
same way as in an older article by this author. We discover some interesting
properties of E and derive five strongly regular graphs from it:
  A srg(256,60,20,12) F which is a subgraph induced by 256 vertices and four
srg(336,80,28,16) H, H_1, H_2 and H_3 which do have E as induced subgraph.
  The latter three graphs are new in version 4 of this article and seem to have
been completely unknown as H was before version 1 appeared. The graph F is
isomorphic to objects described as unions of 16 16-cocliques in a description
of subgraphs of the G2(4) graph by Andries E. Brouwer; but the strong
regularity has been unnoticed before version 1 of this article.
  Several propositions in this article have been checked by executing the
additionally (in the source package) provided program G24DGS2 and the program
Dreadnaut from the popular graph theoretic software nauty (by Brendan McKay and
Adolfo Piperno).
