We present an analysis of the galactocentric distributions of the 'normal' and peculiar '91bg-like' subclasses of 109 supernovae (SNe) Ia, and study the global parameters of their elliptical hosts. The galactocentric distributions of the SN subclasses are consistent with each other and with the radial light distribution of host stellar populations, when excluding bias against central SNe. Among the global parameters, only the distributions of u - r colours and ages are inconsistent significantly between the ellipticals of different SN Ia subclasses: the normal SN hosts are on average bluer/younger than those of 91bg-like SNe. In the colour-mass diagram, the tail of colour distribution of normal SN hosts stretches into the Green Valley - transitional state of galaxy evolution, while the same tail of 91bg-like SN hosts barely reaches that region. Therefore, the bluer/younger ellipticals might have more residual star formation that gives rise to younger 'prompt' progenitors, resulting in normal SNe Ia with shorter delay times. The redder and older ellipticals that already exhausted their gas for star formation may produce significantly less normal SNe with shorter delay times, outnumbered by 'delayed' 91bg-like events. The host ages (lower age limit of the delay times) of 91bg-like SNe does not extend down to the stellar ages that produce significant u-band fluxes - the 91bg-like events have no prompt progenitors. Our results favour SN Ia progenitor models such as He-ignited violent mergers that have the potential to explain the observed SN/host properties.