  We deduce direct formulas for the total number of subgroups and the number of
subgroups of a given order of the group $\Bbb{Z}_m\times \Bbb{Z}_n \times
\Bbb{Z}_r \times \Bbb{Z}_s$, where $m,n,r,s\in \Bbb{N}$. The proofs are by some
simple group theoretical and number theoretical arguments based on Goursat's
lemma for groups. Two conjectures are also formulated.
