  The symmetries of surfaces which can be embedded into the symmetries of the
3-dimensional Euclidean space $\mathbb{R}^3$ are easier to feel by human's
intuition. We give the maximum order of finite group actions on $(\mathbb{R}^3,
\Sigma)$ among all possible embedded closed/bordered surfaces with given
geometric/algebraic genus $>1$ in $\mathbb{R}^3$. We also identify the
topological types of the bordered surfaces realizing the maximum order, and
find simple representative embeddings for such surfaces.
