Fano plane duality group
= Fano plane duality group
{c}
{title2=$GL_3(2)\rtimes\langle\tau\rangle,\quad|\overline G|=336$}
Adjoin the <inverse-transpose automorphism> to the collineation group of the <Fano plane>. Its maximal subgroups other than the collineation group are unordered incident-pair stabilizers, unordered nonincident-pair stabilizers and Sylow 7-normalizers, of orders 16, 12 and 42.