Let $L\subset \mathbb{Z}$ be the subgroup of $\mathbb{Z}^3$ generated by the elements $(-1,-1,4),(2,4,0),(3,3,8)$. Write $\mathbb{Z}^3/L$ as a direct sum of cyclic groups.

I've tried creating a matrix and row reducing, finding the null space of the matrix, but it doesn't seem to produce an obvious answer.

Any help greatly appreciated!


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