I can't sure what isotopes of silver(107 or 109) was used.
But Silver has non-zero nuclear spin since the number of proton and neutron are not even.
Since we use Silver atom not electron in SG experiment,
I think we need to consider spin of electron and silver nucleus simultaneously.
In Sakurai text book, nuclear spin is considered irrelevant to the result of experiment.
If the nuclear spin is 1/2, the total spin of silver atom will be 1.
And we need to observe 3 lines passing through the inhomogeneous B-field.
I don't know why nuclear spin could be ignored.