Extensions 1→N→G→Q→1 with N=C₃×C₆ and Q=C₂²

Direct product G=N×Q with N=C₃×C₆ and Q=C₂²

		d	ρ	Label	ID
C₂×C₆²		72		C2xC6^2	72,50

Semidirect products G=N:Q with N=C₃×C₆ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆)⋊C₂² = C₂×S₃²	φ: C₂²/C₁ → C₂² ⊆ Aut C₃×C₆	12	4+	(C3xC6):C2^2	72,46
(C₃×C₆)⋊₂C₂² = S₃×C₂×C₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	24		(C3xC6):2C2^2	72,48
(C₃×C₆)⋊₃C₂² = C₂²×C₃⋊S₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	36		(C3xC6):3C2^2	72,49

Non-split extensions G=N.Q with N=C₃×C₆ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆).₁C₂² = S₃×Dic₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₃×C₆	24	4-	(C3xC6).1C2^2	72,20
(C₃×C₆).₂C₂² = C₆.D₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₃×C₆	12	4+	(C3xC6).2C2^2	72,21
(C₃×C₆).₃C₂² = D₆⋊S₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₃×C₆	24	4-	(C3xC6).3C2^2	72,22
(C₃×C₆).₄C₂² = C₃⋊D₁₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₃×C₆	12	4+	(C3xC6).4C2^2	72,23
(C₃×C₆).₅C₂² = C₃²⋊₂Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₃×C₆	24	4-	(C3xC6).5C2^2	72,24
(C₃×C₆).₆C₂² = C₃×Dic₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	24	2	(C3xC6).6C2^2	72,26
(C₃×C₆).₇C₂² = S₃×C₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	24	2	(C3xC6).7C2^2	72,27
(C₃×C₆).₈C₂² = C₃×D₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	24	2	(C3xC6).8C2^2	72,28
(C₃×C₆).₉C₂² = C₆×Dic₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	24		(C3xC6).9C2^2	72,29
(C₃×C₆).₁₀C₂² = C₃×C₃⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	12	2	(C3xC6).10C2^2	72,30
(C₃×C₆).₁₁C₂² = C₃²⋊₄Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6).11C2^2	72,31
(C₃×C₆).₁₂C₂² = C₄×C₃⋊S₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	36		(C3xC6).12C2^2	72,32
(C₃×C₆).₁₃C₂² = C₁₂⋊S₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	36		(C3xC6).13C2^2	72,33
(C₃×C₆).₁₄C₂² = C₂×C₃⋊Dic₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	72		(C3xC6).14C2^2	72,34
(C₃×C₆).₁₅C₂² = C₃²⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₃×C₆	36		(C3xC6).15C2^2	72,35
(C₃×C₆).₁₆C₂² = D₄×C₃²	central extension (φ=1)	36		(C3xC6).16C2^2	72,37
(C₃×C₆).₁₇C₂² = Q₈×C₃²	central extension (φ=1)	72		(C3xC6).17C2^2	72,38

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