  The $e^+e^- \rightarrow ZH$ process is the dominant process for the Higgs
boson production at the future Higgs factory. In order to match the analysis on
the Higgs properties with the highly precise experiment data, it will be
crucial to include the theoretical prediction to the full
next-to-next-to-leading order electroweak effect in the production rate
$\sigma(e^+e^-\rightarrow ZH)$. In this inspiring work, we categorize the
two-loop Feynman diagrams of the $\mathcal O(\alpha^2)$ correction to $e^+e^-
\rightarrow ZH$ into 6 categories according to the relevant topological
structures. Although 25377 diagrams contribute to the $\mathcal O(\alpha^2)$
correction in total, the number of the most challenging diagrams with seven
denominators is 2250, which contain only 312 non-planar diagrams with 155
independent types. This categorization could be a valuable reference for the
complete calculation in the future.
