Hypothesis snHG : H <| G.
Hypothesis snKG : K <| G.

(* Specifications: *)
Theorem third_isom : {f : {morphism (G / H) / (K / H) >-> coset_of K} | 'injm f
& forall A : {set gT}, A \subset G -> f @* (A / H / (K / H)) = A / K}.
Theorem third_isog : (G / H / (K / H)) \isog (G / K).
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.