  Let $H$ be the Hopf algebra $H_{c: \sigma_{0}}$ of Kashina [J. Algebra,
232(2000),pp.617-663]. We give all simple Yetter-Drinfel'd modules $V$ over
$H$, then classify all finite-dimensional Nichols algebras of $V$. The finite
dimensional Nichols algebras of diagonal type are either $A_{1}, A_{2}$ or
quantum planes, and non-diagonal type ones are $8$ or $16$ dimensional.
