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We present an analysis of the light curve (LC) decline rates $(\Deltam_{15})$ of 407 normal and peculiar supernovae (SNe) Ia and global parametersof their host galaxies. As previously known, there is a significant correlationbetween the $\Delta m_{15}$ of normal SNe Ia and global ages (morphologies,colours, masses) of their hosts. On average, those normal SNe Ia that are ingalaxies from the Red Sequence (early-type, massive, old hosts) have fasterdeclining LCs in comparison with those from the Blue Cloud (late-type, lessmassive, younger hosts) of the colour-mass diagram. The observed correlationsbetween the $\Delta m_{15}$ of normal SNe Ia and hosts' parameters appear to bedue to the superposition of at least two distinct populations of faster andslower declining normal SNe Ia from older and younger stellar components. Weshow, for the first time, that the $\Delta m_{15}$ of 91bg- and 91T-like SNe isindependent of host morphology and colour. The distribution of hosts on thecolour-mass diagram confirms the known tendency for 91bg-like SNe to occur inglobally red/old galaxies while 91T-like events prefer blue/younger hosts. Onaverage, the youngest global ages of 02cx-like SNe hosts and their positions inthe colour-mass diagram hint that these events likely originate from youngpopulation, but they differ from 91T-like events in the LC decline rate.Finally, we discuss the possible explosion channels and present our favoured SNIa models that have the potential to explain the observed SN-host relations.

Supernovae and their host galaxies -- VII. The diversity of Type Ia supernova progenitors