Hello,

If you're talking about groups with + not *, I think I can help...

The cardinal of the ideal divides the cardinal of the original set, here it's Z/6Z

Hence, the ideals have possible cardinals : 1,2,3,6.

This also helps in finding the elements of the ideals : starting from 0, the following element of the ideal will be , if we work in Z/nZ.

For example, the ideal of Z/6Z which has 3 elements will be the set of elements x such as :

This means that the ideal of Z/6Z with 3 elements is :

I hope this is clear enough