We present measurements of the normalized redshift-space three-point correlation function (3PCF) (Qz) of galaxies from the Sloan Digital Sky Survey (SDSS) main galaxy sample. These measurements were possible because of a fast new N-point correlation function algorithm (called npt) based on multiresolutional k-d trees. We have applied npt to both a volume-limited (36 738 galaxies with 0.05 ≤z≤ 0.095 and −23 ≤M 0.0r≤−20.5) and magnitude-limited sample (134 741 galaxies over 0.05 ≤z≤ 0.17 and ∼M*± 1.5) of SDSS galaxies, and find consistent results between the two samples, thus confirming the weak luminosity dependence of Qz recently seen by other authors. We compare our results to other Qz measurements in the literature and find it to be consistent within the full jackknife error estimates. However, we find these errors are significantly increased by the presence of the ‘Sloan Great Wall’ (at z∼0.08) within these two SDSS data sets, which changes the 3PCF by 70 per cent on large scales (s≥ 10 h−1Mpc). If we exclude this supercluster, our observed Qz is in better agreement with that obtained from the 2-degree Field Galaxy Redshift Survey (2dFGRS) by other authors, thus demonstrating the sensitivity of these higher order correlation functions to large-scale structures in the Universe. This analysis highlights that the SDSS data sets used here are not ‘fair samples’ of the Universe for the estimation of higher order clustering statistics and larger volumes are required. We study the shape dependence of Qz(s, q, θ) as one expects this measurement to depend on scale if the large-scale structure in the Universe has grown via gravitational instability from Gaussian initial conditions. On small scales (s≤ 6 h−1Mpc), we see some evidence for shape dependence in Qz, but at present our measurements are consistent with a constant within the errors (Qz≃ 0.75 ± 0.05). On scales >10 h−1Mpc, we see considerable shape dependence in Qz. However, larger samples are required to improve the statistical significance of these measurements on all scales.