Here's a problem from the Spring 2020 UCLA Algebra Area Exam:
If $K\neq \mathbb{Q}$ appears as a subfield (sharing the identity) of some central simple algebra over $\mathbb{Q}$ of $\mathbb{Q}$-dimension 9, determine (isomorphism classes of) the groups appearing as the Galois group of the Galois closure of $K$ over $\mathbb{Q}$
Since $9=\dim_\mathbb{Q}{R}=\dim_K{R}\cdot\dim_\mathbb{Q}{K}$, I've deduced that $[K:\mathbb{Q}]=3$. Therefore, the Galois group of the Galois closure of $K$ over $\mathbb{Q}$ is either of order 6 or 3. Otherwise, I'm not sure how to use the fact that $K$ is a central simple algebra over $\mathbb{Q}$ to determine the isomorphism class of the Galois group. I'm not looking for an explicit solution, but any small hints are appreciated!