  We describe all the fine group gradings, up to equivalence, on the Lie
algebra $\mathfrak d_4$. This problem is equivalent to finding the maximal
abelian diagonalizable subgroups of the automorphism group of $\mathfrak d_4$.
We prove that there are fourteen by using two different viewpoints. The first
approach is computational: we get a full description of the gradings by using a
particular implementation of the automorphism group of the Dynkin diagram of
$\mathfrak d_4$ and some algebraic groups stuff. The second approach, more
qualitative, emphasizes some algebraic aspects, as triality, and it is mostly
devoted to gradings involving the outer automorphisms of order three.
