**Definition**: Let $G$ be a finite solvable group and $\Sigma \in \text{H}(G)$, the set of Hall systems of $G$. The normaliser of $\Sigma$ is defined as $$ N_G(\Sigma) = \{ g\in G \,|\, H=H^g \text{ for all} H \in \Sigma \}.$$ A system normaliser of $G$ is a subgroup of the form $N_G(\Sigma)$ for some $\Sigma \in \text{H}(G)$.

I have shown that a system normalizer of a finite solvable group covers the central chief factors and avoids the eccentric chief factors of $G$.

**Lemma**: Let $U$ be a subgroup of a finite group $G$. Let $W \leq V \leq G$. Then $V/W$ is covered by $U$ $\iff$ $[U \cap V: U \cap W]=[V:W]$

Theorem: The order of the system normalizer in a finite solvable group is the product of the order of the central chief factors in a chief series of $G$. [Reference:Finite Soluble Groupsby Doerk and Hawkes]

I can't seem to reason why this is the case. The author says that it should follow easily from the lemma but I don't understand how.