We consider the solution of a class of second-order ordinary differential equations not possessing Lie point symmetries by group theoretic means. The method involves increasing the order of these equations using homogeneity symmetry. The solution of this new third-order equation is then sought in the instances that it and the new reduced second-order equation possess additional symmetries. As a result the number of second-order equations solvable by the Lie theory of extended groups is increased.