The 12C(12C,pγ)23Na reaction has been used to study the γ-ray deexcitation of levels up to Ex = 10.4 MeV in 23Na. Doppler-shift attenuation measurements yielded mean lifetimes or lifetime limits for 22 levels. Branching ratios were obtained for the 5.54, 6.11, 6.24, and 6.35 MeV levels and the major modes of decay were observed for 7 levels above Ex = 7 MeV. Angular distributions were measured for γ rays in coincidence with proton groups corresponding to the 5.54, 6.11, 6.24, 6.35, 9.04, and 10.35 MeV levels. The 6.35 MeV level is assigned a spin and parity of 9/2− and interpreted as a member of the low-lying Kπ = 1/2− band in 23Na. Levels at 9.04 and 10.35 MeV are interpreted as the 15/2+ and 13/2− members of the ground-state rotational band and Kπ = 1/2− band, respectively. The experimental γ-ray transition strengths in 23Na are compared to those predicted by the Nilsson model including band mixing. The M1 strengths are modified to account for the effects of isospin.