Cyclic Paths on Sierpiński Graphs

• A Sierpiński graph of order-1 ($S_1$) is an equilateral triangle.
• $S_{n+1}$ is obtained from $S_n$ by positioning three copies of $S_n$ so that every pair of copies has one common corner.

Let $C(n)$ be the number of cycles that pass exactly once through all the vertices of $S_n$.
For example, $C(3)=8$ because eight such cycles can be drawn on $S_3$, as shown below:

It can also be verified that :
$C(1)=C(2)=1$ $C(5)=71328803586048$ $C(10000)\bmod 10^8=37652224$ $C(10000)\bmod 13^8=617720485$

Find $C(C(C(10000)))\bmod 13^8$.