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We present an analysis of the light curve (LC) decline rates $(Δm_{15})$ of 407 normal and peculiar supernovae (SNe) Ia and global parameters of their host galaxies. As previously known, there is a significant correlation between the $Δm_{15}$ of normal SNe Ia and global ages (morphologies, colours, masses) of their hosts. On average, those normal SNe Ia that are in galaxies from the Red Sequence (early-type, massive, old hosts) have faster declining LCs in comparison with those from the Blue Cloud (late-type, less massive, younger hosts) of the colour-mass diagram. The observed correlations between the $Δm_{15}$ of normal SNe Ia and hosts' parameters appear to be due to the superposition of at least two distinct populations of faster and slower declining normal SNe Ia from older and younger stellar components. We show, for the first time, that the $Δm_{15}$ of 91bg- and 91T-like SNe is independent of host morphology and colour. The distribution of hosts on the colour-mass diagram confirms the known tendency for 91bg-like SNe to occur in globally red/old galaxies while 91T-like events prefer blue/younger hosts. On average, the youngest global ages of 02cx-like SNe hosts and their positions in the colour-mass diagram hint that these events likely originate from young population, but they differ from 91T-like events in the LC decline rate. Finally, we discuss the possible explosion channels and present our favoured SN Ia models that have the potential to explain the observed SN-host relations.