Consider a group G = {1,3,5,7,11,13,17} under the multiplication modulo 18 .
Now this group is CYCLIC and have two generators : 5 and 11..
5^1 = 5
5^2 = 7
5^3 = 17
5^4 = 13
5^5 = 11
5^6 = 1
thus giving it order of 6 which is a divisor of order of G. 6(1) = 6 {hence proving lagrange's theorem...