Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²⋊₇D₈

Direct product G=N×Q with N=C₃ and Q=C₃²⋊₇D₈

		d	ρ	Label	ID
C₃×C₃²⋊₇D₈		72		C3xC3^2:7D8	432,491

Semidirect products G=N:Q with N=C₃ and Q=C₃²⋊₇D₈

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₃²⋊₇D₈) = C₃³⋊₇D₈	φ: C₃²⋊₇D₈/C₃²⋊₄C₈ → C₂ ⊆ Aut C₃	72	C3:1(C3^2:7D8)	432,437
C₃⋊₂(C₃²⋊₇D₈) = C₃³⋊₆D₈	φ: C₃²⋊₇D₈/C₁₂⋊S₃ → C₂ ⊆ Aut C₃	144	C3:2(C3^2:7D8)	432,436
C₃⋊₃(C₃²⋊₇D₈) = C₃³⋊₁₅D₈	φ: C₃²⋊₇D₈/D₄×C₃² → C₂ ⊆ Aut C₃	216	C3:3(C3^2:7D8)	432,507

Non-split extensions G=N.Q with N=C₃ and Q=C₃²⋊₇D₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃²⋊₇D₈) = C₃₆.₁₈D₆	φ: C₃²⋊₇D₈/D₄×C₃² → C₂ ⊆ Aut C₃	216		C3.(C3^2:7D8)	432,191
C₃.₂(C₃²⋊₇D₈) = He₃⋊₇D₈	central stem extension (φ=1)	72	6	C3.2(C3^2:7D8)	432,192

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Extensions 1→N→G→Q→1 with N=C3 and Q=C32⋊7D8