  We present an explicit description of the 'fine group gradings' (i.e. group
gradings which cannot be further refined) of the real forms of the semisimple
Lie algebras $sl(4,\C)$, $sp(4,\C)$, and $o(4,\C)$. All together 12 real Lie
algebras are considered, and the total of 44 of their fine group gradings are
listed.
  The inclusions $sl(4,\C)\supset sp(4,\C)\supset o(4,\C)$ are an important
tool in our presentation. Systematic use is made of the faithful
representations of the three Lie algebras by $4\times 4$ matrices.
