Structural properties of a quadruple perovskite BiMn7O12 were investigated by laboratory and synchrotron X-ray powder diffraction between 10 and 650 K, single-crystal X-ray diffraction at room temperature, differential scanning calorimetry (DSC), second-harmonic generation, and first-principles calculations. Three structural transitions were found. Above T1 = 608 K, BiMn7O12 crystallizes in a parent cubic structure with space group Im3̅. Between 460 and 608 K, BiMn7O12 adopts a monoclinic symmetry with pseudo-orthorhombic metrics (denoted as I2/m(o)), and orbital order appears below T1. Below T2 = 460 K, BiMn7O12 is likely to exhibit a transition to space group Im. Finally, below about T3 = 290 K, a triclinic distortion takes place to space group P1. Structural analyses of BiMn7O12 are very challenging because of severe twinning in single crystals and anisotropic broadening and diffuse scattering in powder. First-principles calculations confirm that noncentrosymmetric structures are more stable than centrosymmetric ones. The energy difference between the Im and P1 models is very small, and this fact can explain why the Im to P1 transition is very gradual, and there are no DSC anomalies associated with this transition. The structural behavior of BiMn7O12 is in striking contrast with that of LaMn7O12 and could be caused by effects of the Bi3+ lone electron pair.