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We deduce direct formulas for the total number of subgroups and the number ofsubgroups 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 somesimple group theoretical and number theoretical arguments based on Goursat'slemma for groups. Two conjectures are also formulated.

The number of subgroups of the group $\Bbb{Z}_m\times \Bbb{Z}_n \times \Bbb{Z}_r \times \Bbb{Z}_s$