Intrinsic hand muscles are innervated by C8 and T1, not C6 and C7, roots.
Kimura
J
J
D006225:Hand / Q000033:anatomy & histology*; D006801:Humans; D008475:Median Nerve / Q000033:anatomy & histology*; D018482:Muscle, Skeletal / Q000294:innervation*; D013126:Spinal Nerve Roots / Q000033:anatomy & histology*