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There used to be once a rather well known and interesting conjecture, that was formulated by Gordon E. Wall:

The number of maximal subgroups of a finite group $G$ does not exceed $|G|$

That conjecture appeared to be false. However, the only information about it, that I was able to find, was this MO answer. It contains the statement, that the conjecture was disproven, and a link to the research in which the counterexamples were found. That link, however, seems to be already dead by the time I got there.

So, my question is, what is the minimal possible order of a counterexample to Wall’s conjecture? Or, in case, if that is unknown yet, the minimal order of a known counterexample to Wall’s conjecture?

I need this kind of information for my collection of disproven conjectures in combinatorics

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I think this is a pretty good summary of what is known: aimath.org/news/wallsconjecture/wall.conjecture.pdf

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