Let

1: {0} < <18> < <3> < and

2: {0} < <24> < <12> < .

The first series has quotient groups of order 4, 6, 3 and the second series has quotient groups of order 3, 2, 12. (see here for details)

Now split 4 into 2 and 2 while 12 into 6 and 2.

Then we can make the first series has a factor group of order 2,2,6,3 and the second series has a factor group 3,2,2,6. Now the resulting isomorphic refinements are:

1: {0} < <36> < <18> < <3> < and

2: {0} < <24> < <12> < <6> < .