Let $n \in \mathbb{N}$, then the order of the Galois Group
of $x^n-2$ coincide with $n \phi(n)$ for $n\in \{ 1 , \dots , 36 \}$
except for $n=\{ 8, 16, 24, 32 \}$ where this order is $\frac{ n \phi (n)}{2}$
and is easy to prove that for $p$ prime we have that the order
of the Galois Group of $x^p-2$ is $p(p-1)$.

What is the order of the Galois Group of $x^n-2 : n\in \mathbb{N}$ is general?

Thanks in advance.