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We prove that the only non-trivial finite subgroups of birationalautomorphism group of non-trivial Severi-Brauer surfaces over the field ofrational numbers are $\mathbb{Z}/3\mathbb{Z}$ and $(\mathbb{Z}/3\mathbb{Z})^2.$Moreover, we show that $(\mathbb{Z}/3\mathbb{Z})^2$ is contained in$\mathrm{Bir}(V)$ for any Severi-Brauer surface $V$ over a field ofcharacteristic zero, and $(\mathbb{Z}/3\mathbb{Z})^3$ is contained in$\mathrm{Bir}(V)$ for any Severi-Brauer surface $V$ over a field ofcharacteristic zero which contains a non-trivial cube root of unity.

Birational automorphism groups of Severi-Brauer surfaces over the field of rational numbers