Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂×C₃²⋊₇D₄

Direct product G=N×Q with N=C₃ and Q=C₂×C₃²⋊₇D₄

		d	ρ	Label	ID
C₆×C₃²⋊₇D₄		72		C6xC3^2:7D4	432,719

Semidirect products G=N:Q with N=C₃ and Q=C₂×C₃²⋊₇D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂×C₃²⋊₇D₄) = C₂×C₃³⋊₇D₄	φ: C₂×C₃²⋊₇D₄/C₂×C₃⋊Dic₃ → C₂ ⊆ Aut C₃	72		C3:1(C2xC3^2:7D4)	432,681
C₃⋊₂(C₂×C₃²⋊₇D₄) = S₃×C₃²⋊₇D₄	φ: C₂×C₃²⋊₇D₄/C₃²⋊₇D₄ → C₂ ⊆ Aut C₃	72		C3:2(C2xC3^2:7D4)	432,684
C₃⋊₃(C₂×C₃²⋊₇D₄) = C₂×C₃³⋊₆D₄	φ: C₂×C₃²⋊₇D₄/C₂²×C₃⋊S₃ → C₂ ⊆ Aut C₃	144		C3:3(C2xC3^2:7D4)	432,680
C₃⋊₄(C₂×C₃²⋊₇D₄) = C₂×C₃³⋊₁₅D₄	φ: C₂×C₃²⋊₇D₄/C₂×C₆² → C₂ ⊆ Aut C₃	216		C3:4(C2xC3^2:7D4)	432,729

Non-split extensions G=N.Q with N=C₃ and Q=C₂×C₃²⋊₇D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂×C₃²⋊₇D₄) = C₂×C₆.D₁₈	φ: C₂×C₃²⋊₇D₄/C₂×C₆² → C₂ ⊆ Aut C₃	216		C3.(C2xC3^2:7D4)	432,397
C₃.₂(C₂×C₃²⋊₇D₄) = C₂×He₃⋊₇D₄	central stem extension (φ=1)	72		C3.2(C2xC3^2:7D4)	432,399

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