706
23,328 Rules
(sh.itjust.works)
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Hilarious as all the other answers are, my guess is that this species has more complex sex chromosomes than the XX/XY variations we're familiar with -- perhaps there are more than 2 slots for the chromosomes to go, and then there are more than 2 options per slot, resulting in the humongous number of options stated in the post.
The number 23328 is at least equal to 2^5 *3^6 so that is likely a good clue to what exactly is going on.