Let U14={1,3,5,9,11,13} , U18={1,5,7,11,13,17}

(Ui is the group of all invert elements for multiplication in Zi)

Is U14 isomorphic to U18?

After a LONG check, I found that all the orders of the elements match orders of elements in the second group, just got down after somebody told me it's not enough for isomorphism. Jeez, what IS enough then?!

Thanks