We conduct a population synthesis study of the common envelope evolution (CEE) of a white dwarf (WD) and an asymptotic giant branch (AGB) star and find that the potential number of type Ia supernovae (SNe Ia) from the core degenerate (CD) and from the double degenerate (DD) scenarios are of the same order of magnitude. For the CD scenario we consider cases where a carbon oxygen rich (CO) AGB core and a CO WD merge during the CEE and leave a WD remnant with a mass of >1.35Mo, and for the DD scenario we count surviving CO WD binary systems that merge within a time of 10 Gyr. When either the AGB core or the WD are oxygen neon rich (ONe) we assume that the outcome might be a peculiar SN Ia. We find that the number of potential peculiar SNe Ia in the channels we study, that do not include peculiar SNe Ia that involve helium WDs or helium donors, is non-negligible, but less than the number of normal SNe Ia. If a SN Ia or a peculiar SN Ia explosion takes place within about million year after CEE, whether in the CD scenario or in the DD scenario, a massive circumstellar matter is present at explosion time. Our results are compatible with the suggestion that Chandrasekhar-mass SNe Ia mostly come from the CD scenario, and sub-Chandrasekhar SNe Ia mostly come from the DD scenario.