Abstract A rare subclass of Type Ia supernovae (SNe Ia), named after the prototype SN 2003fg, includes some of the brightest SNe Ia, often called ”super Chandrasekhar-mass” SNe Ia. We calculate the γ-ray deposition histories and the 56Ni mass synthesized in the explosion, MNi56, for eight 2003fg-like SNe. Our findings reveal that the γ-ray escape time, t0, for these objects is t0 ≈ 45–60 days, significantly higher than that of normal SNe Ia. 2003fg-like SNe are distinct from normal SNe Ia in the t0–MNi56 plane, with a noticeable gap between the two populations. The observed position of 2003fg-like SNe in this plane poses a significant challenge for theoretical explosion models. We demonstrate that the merger of two white dwarfs (WDs) and a single star exceeding the Chandrasekhar limit fail to reproduce the observed t0–MNi56 distribution. However, preliminary calculations of head-on collisions of massive WDs show agreement with the observed t0–MNi56 distribution.