  In this paper, we consider the Drinfeld double $\D$ of a $12$-dimensional
Hopf algebra $\C$ over an algebraically closed field of characteristic zero
whose coradical is not a subalgebra and describe its simple modules, projective
covers of the simple modules and show that it is of wild representation type.
Moreover, we show that the Nichols algebras associated to non-simple
indecomposable modules are infinite-dimensional. In particular, for any object
$V$ in $\CYD$, if $\BN(V)$ is finite-dimensional, then $V$ must be semisimple.
Finally, we describe the Nichols algebras associated to partial simple modules
in terms of generators and relations. As a byproduct, we obtain some Hopf
algebras of dimension $72$ without the Chevalley property, that is, the
coradical is not a subalgebra.
