In this link here it says that a cycle be decomposed a product of disjoint cycles. However say you consider the element of $S_4$ (The symmetric group of order 24) given by
$(12)(13)(14) = (1432)$. How would you write this as a product of disjoint cycles? An element in $S_4$ is either of the form $(1),(12),(123),(12)(43)$ or $(1234)$. So looking at the last cycle type we can never decompose it into a disjoint cycle unless we have something like $(1)(234)$. However if you decompose it into the form $(1)(234)$ or say $(14)(23)$ would this not contradict it being of the last cycle type?