2020 Fermat Problem 21

In the diagram, the central circle contains the number 36. Positive integers are to be written in the eight empty circles, one number in each circle, so that the product of the three integers along any straight line is 2592. If the nine integers in the circles must be all different, what is the largest possible sum of these nine integers?

\textbf{(A)}\ 160\quad \textbf{(B)}\ 176\quad \textbf{(C)}\ 178\quad \textbf{(D)}\ 195\quad \textbf{(E)}\ 216

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.