Finite not implies composition factor-unique

Statement
The order of the composition factors for different composition series of a finite group need not be the same. In other words, it is possible to have two composition series:

$$\{ e \} = M_0 \le M_1 \le \dots \le M_r = G$$

and

$$\{ e \} = N_0 \le N_1 \le \dots \le N_r = G$$.

such that there is some $$i$$ for which $$N_i/N_{i-1}$$ is not isomorphic to $$M_i/M_{i-1}$$.

Example of a direct product of simple groups
Let $$G_1, G_2$$ be non-isomorphic simple groups. Then, the group $$G = G_1 \times G_2$$ has the two composition series:

$$M_0 = \{ e \} \le M_1 = G_1 \times \{ e \} \le M_2 = G_1 \times G_2$$

and:

$$N_0 = \{ e \} \le N_1 = \{ e \} \times G_2 \le N_2 = G_1 \times G_2$$.

The quotients for the two series come in different orders: in the first series. For the first series, the quotient $$M_1/M_0$$ is $$G_1$$ and the quotient $$M_2/M_1$$ is $$G_2$$. For the second series, the quotient $$N_1/N_0$$ is $$G_2$$ and the quotient $$N_2/N_1$$ is $$G_1$$. Since $$G_1$$ is not isomorphic to $$G_2$$, the quotients do not occur in the same order.