  Let $p\geq 5$ be a prime number, let $n\geq 2$ be a natural number and let
$\text{Heis}(p^n)$ denote the Heisenberg group modulo $p^n$. We study the
Lyndon-Hochschild-Serre spectral sequence $E(\text{Heis}(p^n))$ associated to
$\text{Heis}(p^n)$ considered as a split extension, and show that,
$E(\text{Heis}(p^n))$ collapses in the third page. Moreover, for a fixed $p$,
the spectral sequences $E(\text{Heis}(p^n))$ are isomorphic from the second
page on.
