Are $G/A$ and $G/B$ isomorphic if $A$ and $B$ have the same order?
I think so but want to confirm. Let $G$ be finite.
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2No, it's "very" false - why don't you try to think up some examples? – peter a g Oct 31 '16 at 12:13
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@peterag Okay, thanks for the reply. I may still be off, but would it be true if we added that $G/A$ and $G/B$ are both simple? – CuriousKid7 Oct 31 '16 at 12:59
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That would amount to the claim that finite simple groups of the same order are isomorphic, which is not true. – Tobias Kildetoft Oct 31 '16 at 13:02