Why is the number of the conjugacy classes of $D_4 \rtimes Aut(D_4)$ $16$?

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Currently, I am reading Representation Theory of Semi-Direct Products by Reyes.

In section $6$, the author mentions that the number of the conjugacy classes of $D_4 \rtimes Aut(D_4)$ is $16$. My question is why $16$?

I don't even know where to start.