Aluffi IV.3.2 goes as follows:
Let $G$ be a finite cyclic group. Compute $\ell(G)$ in terms of $|G|$. Generalize to finite solvable groups.
Here $\ell(G)$ is the maximal length of a normal series in $G$.
First part looks straightforward: cyclic groups are abelian, so if $|G| = p_1^{k_1} \dots p_n^{k_n}$, then $\ell(G) = k_1 + \dots + k_n$.
But what about finite solvable groups? I don't think I see how to connect $\ell(G)$ with $|G|$ for them.