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No, that's not my example. I think of an example where ##G/H## is not simple, e.g. the sum of simple groups, ##H## is maximal solvable and normal, and all subgroups that contain ##H## are not normal.Office_Shredder said:Is your assertion here that there is a subgroup ##K\subset G/N## that cannot be written as ##K'/N## for some ##K'\subset G##? I think this is false - ##K'=KN## should work (also the statement of the correspondence theorem is that it is a bijection)