Treat the vowels A, I, O as a single unit or 'super letter'. This reduces the problem to arranging 11 units: the 'super letter' and the consonants C, C, M, M, D, T, N.

The number of ways to arrange these 11 units is given by:

\(\frac{8!}{2!2!}\)

The 'super letter' contains the vowels A, A, O, O, O, I, which can be arranged in:

\(\frac{6!}{2!3!}\)

Therefore, the total number of arrangements is:

\(\frac{8!}{2!2!} \times \frac{6!}{2!3!} = 604800\)