I want to find an example of a finite group $G$, which has two non-conjugate $\pi$-subgroups of Hall.
From the Hall's theorem I know that I have to search in the class of non-solvable groups. So my $G$ has order at least $60$ and it is divisible for at least three distinct prime numbers. My idea was to find a group with two subgroups $H_1$ and $H_2$ of the proper order to be $\pi$ -subgroups of Hall and such that one of them was normal in $G$ and the other was not. But I got stuck.
I would be very thankful if someone could help me finding this example.