Trascendental extension over the complex field

Question

Let t be a variable and consider the extension over $\mathbb{C}$, $\mathbb{C}(t)/\mathbb{C}(t^{12})$. I have already proven that it's a Galois extension. I want to find the Galois group. I know it must have order since since the irreducible over $\mathbb{C}(t)$ is $x^{12}-t^{12}$. Now this gives me a lot of options with groups of order 12. Any ideas on how to proceed?