Polynomial growth conjecture for maximal arithmetic subgroups

Let $H$ be a connected semi-simple Lie group without almost simple factors of type $\mathrm{A}_1$ and without compact factors. For sufficiently large $x$, consider maximal irreducible arithmetic subgroups of $H$ whose covolumes are less than $x$. Polynomial growth conjecture for maximal arithmetic subgroups. There exists a constant $B_H>0$, depending only on the types of the almost simple factors of $H$, such that the number of their conjugacy classes is at most $x^{B_H}$. This is the polynomial upper bound asserted for the counting function of maximal irreducible arithmetic subgroups; the supplied text gives no evidence that it has been resolved.