Semisymmetric cubic graphs of twice odd order

Connected cubic graphs Gamma of twice odd order which admit an automorphism group acting semisytnmetrically are investigated. The structure of the automorphism group of Gamma modulo a subgroup which acts semiregularly on Gamma 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. (c) 2005 Elsevier Ltd. All rights reserved.