Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²⋊₇Q₁₆

Direct product G=N×Q with N=C₃ and Q=C₃²⋊₇Q₁₆

		d	ρ	Label	ID
C₃×C₃²⋊₇Q₁₆		144		C3xC3^2:7Q16	432,494

Semidirect products G=N:Q with N=C₃ and Q=C₃²⋊₇Q₁₆

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₃²⋊₇Q₁₆) = C₃³⋊₇Q₁₆	φ: C₃²⋊₇Q₁₆/C₃²⋊₄C₈ → C₂ ⊆ Aut C₃	144	C3:1(C3^2:7Q16)	432,446
C₃⋊₂(C₃²⋊₇Q₁₆) = C₃³⋊₆Q₁₆	φ: C₃²⋊₇Q₁₆/C₃²⋊₄Q₈ → C₂ ⊆ Aut C₃	144	C3:2(C3^2:7Q16)	432,445
C₃⋊₃(C₃²⋊₇Q₁₆) = C₃³⋊₁₅Q₁₆	φ: C₃²⋊₇Q₁₆/Q₈×C₃² → C₂ ⊆ Aut C₃	432	C3:3(C3^2:7Q16)	432,510

Non-split extensions G=N.Q with N=C₃ and Q=C₃²⋊₇Q₁₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃²⋊₇Q₁₆) = C₃₆.₁₉D₆	φ: C₃²⋊₇Q₁₆/Q₈×C₃² → C₂ ⊆ Aut C₃	432		C3.(C3^2:7Q16)	432,194
C₃.₂(C₃²⋊₇Q₁₆) = He₃⋊₇Q₁₆	central stem extension (φ=1)	144	6	C3.2(C3^2:7Q16)	432,197

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Extensions 1→N→G→Q→1 with N=C3 and Q=C32⋊7Q16