The study of the (non)-existence of integral Hopf orders was originally motivated by Kaplansky's sixth conjecture, which is a generalization of a Frobenius theorem in the Hopf algebra setting. In fact, Larson proved that a Hopf algebra which admits an integral Hopf order satisfies the conjecture. The aim of this talk is to give a partial answer to the following question: Does a semisimple complex Hopf algebra admit an integral Hopf order? In particular, we will present several families of semisimple Hopf algebras which do not admit an integral Hopf order. These Hopf algebras will be constructed as Drinfeld twists of group algebras. This talk is based on a joint work with Giovanna Carnovale and Juan Cuadra, and on my Ph.D. thesis.