Section SecondIsomorphism.
Variables (gT : finGroupType) (H K : {group gT}).
Hypothesis nKH : H \subset 'N(K).
Hypothesis sHK : H \subset K.
Hypothesis snHG : H <| G.
Hypothesis snKG : K <| G.
End ThirdIsomorphism.

Lemma char_from_quotient (gT : finGroupType) (G H K : {group gT}) :
H <| K -> H \char G -> K / H \char G / H -> K \char G.