The weak Malle conjecture over the rationals

Let $G$ be a transitive subgroup of $S_n$. Let $\mathcal F_n(X;G)$ be the set of degree-$n$ number fields $K$ satisfying

$$[K:\mathbb Q]=n,\qquad \operatorname{Gal}(\hat K/\mathbb Q)=G,\qquad |\Delta_K|\leqslant X,$$

where $\hat K$ is the Galois closure of $K$ over $\mathbb Q$, and equality of Galois groups is up to conjugacy as permutation groups on the $n$ embeddings of $K$. Write $F_n(X;G)=|\mathcal F_n(X;G)|$. Define

$$\operatorname{ind}(G)=\min\{\operatorname{ind}(g):1\ne g\in G\},$$

where $n-\operatorname{ind}(g)$ is the number of orbits of $g$ on $\{1,2,\ldots,n\}$, and set $a(G)=\operatorname{ind}(G)^{-1}$. Weak Malle conjecture over the rationals. For every $\varepsilon>0$,

$$X^{a(G)}\ll_n F_n(X;G)\ll_{n,\varepsilon}X^{a(G)+\varepsilon}.$$

This is a weakened form of Malle's conjecture, stated in response to Klüners's counterexample to the original formulation. The source attributes this version to Alb20; the general conjecture is not presented as resolved here.