Semisymmetric cubic graphs of twice odd order

Connected cubic graphs Γ of twice odd order which admit an automorphism group acting semisymmetrically are investigated. The structure of the automorphism group of Γ modulo a subgroup which acts semiregularly on Γ is determined. This identification is achieved by using the fundamental theorem of Goldschmidt [D.M. Goldschmidt, Automorphisms of trivalent graphs, Ann. of Math. (2) 111 (2) (1980) 377–406] and some small parts of the proof of the classification of the finite simple groups.