Neumann–Praeger conjecture on Kronecker classes

Let $G$ be a finite group with subgroups $U$ and $U'$, and let $n=|G:U'|$. For a subgroup $V$ of $G$, write $V^g=g^{-1}Vg$ and let $\bigcup_{g\in G}V^g$ denote the union of its conjugates. Neumann–Praeger conjecture. There exists a function $f$ such that, if

$$\bigcup_{g\in G}U^g=\bigcup_{g\in G}(U')^g,$$

then

$$|G:U|\leq f(n).$$

In the arithmetic interpretation, equality of these conjugate unions is equivalent to Kronecker equivalence of the corresponding field extensions, so the conjecture predicts that the degree of a field in a Kronecker class is bounded in terms of the degree of another member. The supplied text gives no resolution status.