Let $G$ be an affine algebraic group over $\mathbb{C}$. According to SGA3, any closed normal subgroup $N$ is representable by an affine algebraic group, as is the quotient $G/N$.

These statements are valid in the fpqc topology: that is, they are true when considering algebraic groups as group objects in the category of sheaves on the big (affine) fpqc site of $\mathrm{Spec}\;\mathbb{C}$. My question is:

Can I lift this to the étale topology?

Even if this cannot be done in general, is there a know set of conditions on $G$ (maybe on $N$ too) that guarantees that the map $G \to G/N$ is also a quotient in the étale topology?

closednormal subgroup scheme $N$ of $G$, is there an fppf (hence fpqc!) homomorphism of affine algebraic groups $G\rightarrow Q$ with kernel $N$, and if so then is $G\rightarrow Q$ also etale? The 1st is affirmative overanyfield (use generic flatness and geometric translations), the 2nd is an exercise in fppf descent theory since $N$ is smooth (char. 0!). – user29283 Jun 11 '13 at 23:55surjectionshave etale-local sections.QED – user29720 Jun 13 '13 at 3:20