The nerves that go to the sacroiliac joint also go to the surrounding muscles, specifically the dorsal branches of S1-S2 and the ventral branches of L4 to S2 with occasionally S3 and rarely L3, but most commonly L4 to L5 and the superior gluteal nerve (L4 to S1) [1].

However, since there are different studies finding multiple variations, the exact innervation is unclear [2].

Additionally, even within the same individual, the right and left sides may have different innervation [3]P434.

References

1. Solonen, K.A., The sacroiliac joint in the light of anatomical, roentgenological and clinical studies. Acta Orthopaedica Scandinavica. Supplementum, 1957. 27(Suppl 27): p. 1-127.<br />
2. Foley, B.S. and R.M. Buschbacher, Sacroiliac joint pain: anatomy, biomechanics, diagnosis, and treatment. Am J Phys Med Rehabil, 2006. 85(12): p. 997-1006.<br />
3. Haldeman, S., et al., eds. Principles and Practice of Chiropractic. 3rd ed. 2005, McGraw-Hill