Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.) $\textbf {(A)}\ 210 \qquad$ $ \textbf {(B)}\ 560 \qquad$ $ \textbf {(C)}\ 840 \qquad$ $ \textbf {(D)}\ 1260 \qquad$ $ \textbf {(E)}\ 1680$