  A fundamental theorem in graph theory states that any 3-connected graph
contains a subdivision of $K_4$. As a generalization, we ask for the minimum
number of $K_4$-subdivisions that are contained in every $3$-connected graph on
$n$ vertices. We prove that there are $\Omega(n^3)$ such $K_4$-subdivisions and
show that the order of this bound is tight for infinitely many graphs. We
further investigate a better bound in dependence on $m$ and prove that the
computational complexity of the problem of counting the exact number of
$K_4$-subdivisions is $\#P$-hard.
