I know that with prime ordered Elliptic Curve Groups, the Elliptic Curve Discrete Logarithm Problem (ECDLP) can be solved easily by defining an isomorphism to the additive group of integers mod $p$ where $p$ is the order of the group. The ECDLP is transformed into a simpler matter of performing the Extended Euclidean algorithm. However, for non-prime ordered groups, can a similar isomorphism to the additive group of integers be defined?
Would one need to compute the order of a point X and then define an Isomorphism between the cyclic subgroup generated by X and the group of additive integers modulo the order?