  For a graph $H$, the 1-subdivision of $H$, denoted by $H'$, is the graph
obtained by replacing the edges of $H$ by internally disjoint paths of length
2. Recently, Conlon, Janzer and Lee (arXiv: 1903.10631) asked the following
question: For any integer $s\ge2$, estimate the smallest $t$ such that
$\textup{ex}(n,K_{s,t}')=\Omega(n^{\frac{3}{2}-\frac{1}{2s}})$. In this paper,
we consider the case $s=3$. More precisely, we provide an explicit construction
giving \begin{align*} \text{ex}(n,K_{3,30}')=\Omega(n^{\frac{4}{3}}),
\end{align*} which reduces the estimation for the smallest value of $t$ from a
magnitude of $10^{56}$ to the number $30$. The construction is algebraic, which
is based on some equations over finite fields.
