Puzzle of the Week #487 - How Many Ways

How many ways are there of arranging the digits 1,2,3,4,5,6 such that the first two digits make a multiple of 3, the middle two digits make a multiple of 4 and the final two digits make a multiple of 5?

(Example: 123645, 12=3x4, 36=4x9, 45=5x9)