Let $V$ be a finite dimensional $\mathbb R$-vector space. Suppose that $L\subset V$ is a lattice (i.e. a discrete subgroup) and $M\subset L$ is another lattice, which is also a subgroup of $L$. Moreover assume that the quotient $L/M$ is finite of cardinality $r$. In other words we have the short exact sequence: $$0\to M\to L\to L/M\to 0$$ The volume of a lattice $L$ is defined as: $$\operatorname{vol}(L):=\mu(V/L)$$ where $\mu$ is the Haar measure induced on the quotient (by a fixed Haar measure on $V$). Alternatively $\operatorname{vol}(L)$ is the measure of the so called fundamental region of $L$.
Given the above setting my question is the following:
What is the relationship between the numbers $\operatorname{vol}(L)$, $\operatorname{vol}(M)$ and $r$?
I mean, for a short exact sequence of lattices $$0\to M\to L\to N\to 0$$ we would have $\operatorname{vol}(L)=\operatorname{vol}(M)\cdot\operatorname{vol}(N) $. But what about the case in object?