Color Cube

Given 3 yellow cubes, 6 red cubes, 9 blue cubes, and 9 green cubes, it is possible to make a larger 3x3 cube. How many possible visually different ways are there to construct a 3x3 cube out of the 27 smaller cubes? Note that differences in the non-visible piece in the center do not count as new combinations, swapping pieces of the same color does not count as a new combination, however, different rotations do count as different combinations. (Yes, it's a very large number so you might want a calculator)