  Bhargava, Hanke, and Shankar have recently shown that the asymptotic average
$2$-torsion subgroup size of the family of class groups of monogenized cubic
fields with positive and negative discriminants is $3/2$ and $2$, respectively.
In this paper, we provide strong computational evidence for these asymptotes.
We then develop a pair of novel conjectures that predicts, for $p$ prime, the
asymptotic average $p$-torsion subgroup size in class groups of monogenized
cubic fields.
