Finite symmetries for embeddings of genus $\geq 2$ surfaces in $\mathbb{R}^3$

Question

Let $f : \Sigma \to \mathbb{R}^3$ be a genus $g \geq 2$ surface smoothly embedded in $\mathbb{R}^3$. Let $$ G(f) = \{ \phi \in \text{Isom}(\mathbb{R}^3) : \phi(f(\Sigma)) = f(\Sigma)\} $$ be the group of isometries of $\mathbb{R}^3$ that preserve $\Sigma$. Is the order of $G(f)$ always finite? If so is there a bound on the order of $G(f)$ (presumably in terms of $g$)?