McIver–Neumann conjecture on the enumeration of finite groups

Let $f(n)$ be the number of isomorphism classes of groups of order $n$, and let $\lambda$ be the number of prime divisors of $n$, counted with multiplicities. McIver–Neumann conjecture.

$$f(n) \leq n^{(\frac{2}{27}+\epsilon)\lambda^2}$$

where $\epsilon \to 0$ as $\lambda \to \infty$.

This conjecture concerns the asymptotic number of isomorphism classes of finite groups of a given order and is motivated by results on the enumeration of finite $p$-groups. The supplied source does not state whether the conjecture has been resolved.