Abstract: Using the method of preliminary group classification introduced by Ibragimov et al[J.Math.Phys.32,2988(1991)], we give a classification of equations v_t=f(x, v_x)v_xx+g(x, v_x) which admitting an extension by one of the principal Lie algebra of the equation. The result of this paper is a table of nonequivalent equations possessing an additional symmetry.