Under the Theorem 1.1 and Theorem 1.3 of [split etension](https://www.researchgate.net/publication/337221031_ON_A_SPECIAL_CLASS_OF_FINITE_p-GROUPS_OF_MAXIMAL_CLASS_AND_EXPONENT_p), can be deduced that the  number of  isomorphism  classes  of  splits  extensions of $( \mathbb{Z} / p \mathbb{Z} )^n$ by $\mathbb{Z} / p \mathbb{Z} $ is $P(n)-1$ where $P(n)$ denotes the  number  of  partitions of $n$.


Any help would be appreciated so much. Thank you all.