I have a question about the spontaneous symmetry breaking (SSB) and its effect on the group symmetries of the Standard Model.

If I understand correctly, before SSB (at high temperatures/energies) the initial symmetry was given by:

$$SU(3)\times SU(2)_{L}\times U(1)_{Y}$$ where $SU(2)_{L}\times U(1)_{Y}$ symmetry group describes the electroweak interactions.

After SSB the symmetry broke into: $$SU(3)\times U(1)_{Q}$$

And this is actually what we observe now at room temperature.

My question is the following: Since $SU(3)$ describes the strong interactions, and $U(1)_{Q}$ describes the electromagnetic interactions, (why) isn't there a symmetry group describing the weak interaction (after SSB - so "decoupled" from the electromagnetic interaction)?