It is often stated that rotations in the 3 spatial dimensions are examples of Lorentz transformations.
But Lorentz transformations form a group named the Lorentz Group, $O(1,3)$ which is a group a $4 \times 4$ matrices, $\Lambda$ having the following property:
$$ \Lambda^T g \Lambda = g$$
where $g$ is the metric tensor.
Now rotations matrices for the 3 spatial dimensions are $3 \times 3$ matrices and form $SO(3)$. How can they be in the $O(1,3)$ ?