Extensions 1→N→G→Q→1 with N=C₂×He₃ and Q=C₂²

Direct product G=N×Q with N=C₂×He₃ and Q=C₂²

		d	ρ	Label	ID
C₂³×He₃		72		C2^3xHe3	216,115

Semidirect products G=N:Q with N=C₂×He₃ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×He₃)⋊C₂² = C₂×C₃²⋊D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂×He₃	18	6+	(C2xHe3):C2^2	216,102
(C₂×He₃)⋊₂C₂² = C₂²×C₃²⋊C₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36		(C2xHe3):2C2^2	216,110
(C₂×He₃)⋊₃C₂² = C₂²×He₃⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36		(C2xHe3):3C2^2	216,113

Non-split extensions G=N.Q with N=C₂×He₃ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×He₃).₁C₂² = He₃⋊₂Q₈	φ: C₂²/C₁ → C₂² ⊆ Out C₂×He₃	72	6-	(C2xHe3).1C2^2	216,33
(C₂×He₃).₂C₂² = C₆.S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₂×He₃	36	6	(C2xHe3).2C2^2	216,34
(C₂×He₃).₃C₂² = He₃⋊₂D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₂×He₃	36	6+	(C2xHe3).3C2^2	216,35
(C₂×He₃).₄C₂² = He₃⋊(C₂×C₄)	φ: C₂²/C₁ → C₂² ⊆ Out C₂×He₃	36	6-	(C2xHe3).4C2^2	216,36
(C₂×He₃).₅C₂² = He₃⋊₃D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₂×He₃	36	6	(C2xHe3).5C2^2	216,37
(C₂×He₃).₆C₂² = He₃⋊₃Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	72	6-	(C2xHe3).6C2^2	216,49
(C₂×He₃).₇C₂² = C₄×C₃²⋊C₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36	6	(C2xHe3).7C2^2	216,50
(C₂×He₃).₈C₂² = He₃⋊₄D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36	6+	(C2xHe3).8C2^2	216,51
(C₂×He₃).₉C₂² = C₂×C₃²⋊C₁₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	72		(C2xHe3).9C2^2	216,59
(C₂×He₃).₁₀C₂² = He₃⋊₆D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36	6	(C2xHe3).10C2^2	216,60
(C₂×He₃).₁₁C₂² = He₃⋊₄Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	72	6	(C2xHe3).11C2^2	216,66
(C₂×He₃).₁₂C₂² = C₄×He₃⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36	3	(C2xHe3).12C2^2	216,67
(C₂×He₃).₁₃C₂² = He₃⋊₅D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36	6	(C2xHe3).13C2^2	216,68
(C₂×He₃).₁₄C₂² = C₂×He₃⋊₃C₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	72		(C2xHe3).14C2^2	216,71
(C₂×He₃).₁₅C₂² = He₃⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×He₃	36	6	(C2xHe3).15C2^2	216,72
(C₂×He₃).₁₆C₂² = C₂×C₄×He₃	φ: trivial image	72		(C2xHe3).16C2^2	216,74
(C₂×He₃).₁₇C₂² = D₄×He₃	φ: trivial image	36	6	(C2xHe3).17C2^2	216,77
(C₂×He₃).₁₈C₂² = Q₈×He₃	φ: trivial image	72	6	(C2xHe3).18C2^2	216,80

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