  Normal distribution manifolds play essential roles in the theory of
information geometry, so do holonomy groups in classification of Riemannian
manifolds. After some necessary preliminaries on information geometry and
holonomy groups, it is presented that the corresponding Riemannian holonomy
group of the $d$-dimensional normal distribution is
$SO\left(\frac{d\left(d+3\right)}{2}\right)$, for all $d\in\mathbb{N}$. As a
generalization on exponential family, a list of holonomy groups follows.
