A finite group is $[G:H]$ equal-sized cosets of $H$.Suggest a slogan
Let \(G\) be a finite group, let
\(H\leq G\) be a subgroup, and let \(G/H\) be the set of left cosets of \(H\) in \(G\), so that \([G:H] = \# (G/H)\) is the index of \(H\).
Then \[
\# G = [G:H]\, \# H,
\qquad\text{equivalently}\qquad
[G:H] = \frac{\# G}{\# H}.
\]