Recently , it has been found that off-centre carbon burning in a subset of intermediate-mass stars does not propagate all the way to the center , resulting in a class of hybrid CONe cores . The implications of a significant presence of carbon in the resulting massive degenerate cores have not been thoroughly explored so far . Here , we consider the possibility that stars hosting these hybrid CONe cores might belong to a close binary system and , eventually , become white dwarfs accreting from a non-degenerate companion at rates leading to a supernova explosion . We have computed the hydrodynamical phase of the explosion of Chandrasekhar-mass white dwarfs harboring hybrid cores , assuming that the explosion starts at the center , either as a detonation ( as may be expected in some degenerate merging scenarios ) or as a deflagration ( that afterwards transitions into a delayed detonation ) . We assume these hybrid cores are made of a central CO volume , of mass M _ { \mathrm { CO } } , surrounded by an ONe shell . We show that , in case of a pure detonation , a medium-sized CO-rich region , M _ { \mathrm { CO } } ( < 0.4 M _ { { \sun } } ) , results in the ejection of a small fraction of the mantle while leaving a massive bound remnant . Part of this remnant is made of the products of the detonation , Fe-group nuclei , but they are buried in its inner regions , unless convection is activated during the ensuing cooling and shrinking phase of the remnant . In contrast , and somehow paradoxically , delayed detonations do not leave remnants but for the minimum M _ { \mathrm { CO } } we have explored , M _ { \mathrm { CO } } = 0.2 M _ { \sun } , and even in this case the remnant is as small as 0.13 M _ { { \sun } } . The ejecta produced by these delayed detonations are characterized by slightly smaller masses of ^ { 56 } Ni and substantially smaller kinetic energies than obtained for a delayed detonation of a “ normal ” CO white dwarf . The optical emission expected from these explosions would hardly match the observational properties of typical Type Ia supernovae , although they make interesting candidates for the subluminous class of SN2002cx-like or SNIax .