An example (this is exercise 21exercise 21 in Chapter 2.2 of Borevich and Shafarevich) is given by the three cubic fields obtained by adjoining a root of x^3-18x-6$x^3-18x-6$, x^3-36x-78$x^3-36x-78$ and x^3-54x-150$x^3-54x-150$. The resulting fields are non-isomorphic cubics with class number one and discriminant 22356$22356$.