  A class $\mathcal{F}$ of graphs has the induced Erd\H{o}s-P\'osa property if
there exists a function $f$ such that for every graph $G$ and every positive
integer $k$, $G$ contains either $k$ pairwise vertex-disjoint induced subgraphs
that belong to $\mathcal{F}$, or a vertex set of size at most $f(k)$ hitting
all induced copies of graphs in $\mathcal{F}$. Kim and Kwon (SODA'18) showed
that for a cycle $C_{\ell}$ of length $\ell$, the class of
$C_{\ell}$-subdivisions has the induced Erd\H{o}s-P\'osa property if and only
if $\ell\le 4$. In this paper, we investigate whether or not the class of
$H$-subdivisions has the induced Erd\H{o}s-P\'osa property for other graphs
$H$.
  We completely settle the case when $H$ is a forest or a complete bipartite
graph. Regarding the general case, we identify necessary conditions on $H$ for
the class of $H$-subdivisions to have the induced Erd\H{o}s-P\'osa property.
For this, we provide three basic constructions that are useful to prove that
the class of the subdivisions of a graph does not have the induced
Erd\H{o}s-P\'osa property. Among remaining graphs, we prove that if $H$ is
either the diamond, the $1$-pan, or the $2$-pan, then the class of
$H$-subdivisions has the induced Erd\H{o}s-P\'osa property.
