Extensions 1→N→G→Q→1 with N=C₁₂ and Q=D₄

Direct product G=N×Q with N=C₁₂ and Q=D₄

		d	ρ	Label	ID
D₄×C₁₂		48		D4xC12	96,165

Semidirect products G=N:Q with N=C₁₂ and Q=D₄

extension	φ:Q→Aut N	d	Label	ID
C₁₂⋊₁D₄ = C₁₂⋊D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	C12:1D4	96,102
C₁₂⋊₂D₄ = D₆⋊₃D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	C12:2D4	96,145
C₁₂⋊₃D₄ = C₁₂⋊₃D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	C12:3D4	96,147
C₁₂⋊₄D₄ = C₄⋊D₁₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	C12:4D4	96,81
C₁₂⋊₅D₄ = C₄×D₁₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	C12:5D4	96,80
C₁₂⋊₆D₄ = C₃×C₄⋊₁D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	C12:6D4	96,174
C₁₂⋊₇D₄ = C₁₂⋊₇D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	C12:7D4	96,137
C₁₂⋊₈D₄ = C₄×C₃⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	C12:8D4	96,135
C₁₂⋊₉D₄ = C₃×C₄⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	C12:9D4	96,168

Non-split extensions G=N.Q with N=C₁₂ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁D₄ = C₆.D₈	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.1D4	96,16
C₁₂.₂D₄ = C₆.SD₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	96		C12.2D4	96,17
C₁₂.₃D₄ = C₃⋊D₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	4+	C12.3D4	96,33
C₁₂.₄D₄ = D₈.S₃	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	4-	C12.4D4	96,34
C₁₂.₅D₄ = C₈.₆D₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	4+	C12.5D4	96,35
C₁₂.₆D₄ = C₃⋊Q₃₂	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	96	4-	C12.6D4	96,36
C₁₂.₇D₄ = D₄⋊Dic₃	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.7D4	96,39
C₁₂.₈D₄ = C₁₂.D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	24	4	C12.8D4	96,40
C₁₂.₉D₄ = Q₈⋊₂Dic₃	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	96		C12.9D4	96,42
C₁₂.₁₀D₄ = C₁₂.₁₀D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	4	C12.10D4	96,43
C₁₂.₁₁D₄ = C₄.D₁₂	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.11D4	96,104
C₁₂.₁₂D₄ = C₈⋊D₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	24	4+	C12.12D4	96,115
C₁₂.₁₃D₄ = C₈.D₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	4-	C12.13D4	96,116
C₁₂.₁₄D₄ = C₂×D₄⋊S₃	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.14D4	96,138
C₁₂.₁₅D₄ = D₁₂⋊₆C₂²	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	24	4	C12.15D4	96,139
C₁₂.₁₆D₄ = C₂×D₄.S₃	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.16D4	96,140
C₁₂.₁₇D₄ = C₂³.₁₂D₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.17D4	96,143
C₁₂.₁₈D₄ = C₂×Q₈⋊₂S₃	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.18D4	96,148
C₁₂.₁₉D₄ = Q₈.₁₁D₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48	4	C12.19D4	96,149
C₁₂.₂₀D₄ = C₂×C₃⋊Q₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	96		C12.20D4	96,150
C₁₂.₂₁D₄ = Dic₃⋊Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	96		C12.21D4	96,151
C₁₂.₂₂D₄ = D₆⋊₃Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.22D4	96,153
C₁₂.₂₃D₄ = C₁₂.₂₃D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₁₂	48		C12.23D4	96,154
C₁₂.₂₄D₄ = D₄₈	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	2+	C12.24D4	96,6
C₁₂.₂₅D₄ = C₄₈⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	2	C12.25D4	96,7
C₁₂.₂₆D₄ = Dic₂₄	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	96	2-	C12.26D4	96,8
C₁₂.₂₇D₄ = C₁₂⋊₂Q₈	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	96		C12.27D4	96,76
C₁₂.₂₈D₄ = C₄²⋊₇S₃	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48		C12.28D4	96,82
C₁₂.₂₉D₄ = C₂×C₂₄⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48		C12.29D4	96,109
C₁₂.₃₀D₄ = C₂×D₂₄	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48		C12.30D4	96,110
C₁₂.₃₁D₄ = C₂×Dic₁₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	96		C12.31D4	96,112
C₁₂.₃₂D₄ = C₁₂⋊C₈	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	96		C12.32D4	96,11
C₁₂.₃₃D₄ = C₄²⋊₄S₃	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	24	2	C12.33D4	96,12
C₁₂.₃₄D₄ = C₂₄.C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	2	C12.34D4	96,26
C₁₂.₃₅D₄ = C₄○D₂₄	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	2	C12.35D4	96,111
C₁₂.₃₆D₄ = C₃×D₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	2	C12.36D4	96,61
C₁₂.₃₇D₄ = C₃×SD₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48	2	C12.37D4	96,62
C₁₂.₃₈D₄ = C₃×Q₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	96	2	C12.38D4	96,63
C₁₂.₃₉D₄ = C₃×C₄.₄D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48		C12.39D4	96,171
C₁₂.₄₀D₄ = C₃×C₄⋊Q₈	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	96		C12.40D4	96,175
C₁₂.₄₁D₄ = C₆×D₈	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48		C12.41D4	96,179
C₁₂.₄₂D₄ = C₆×SD₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	48		C12.42D4	96,180
C₁₂.₄₃D₄ = C₆×Q₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₁₂	96		C12.43D4	96,181
C₁₂.₄₄D₄ = C₂.Dic₁₂	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	96		C12.44D4	96,23
C₁₂.₄₅D₄ = C₂.D₂₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48		C12.45D4	96,28
C₁₂.₄₆D₄ = C₁₂.₄₆D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	24	4+	C12.46D4	96,30
C₁₂.₄₇D₄ = C₁₂.₄₇D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	4-	C12.47D4	96,31
C₁₂.₄₈D₄ = C₁₂.₄₈D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48		C12.48D4	96,131
C₁₂.₄₉D₄ = D₄⋊D₆	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	24	4+	C12.49D4	96,156
C₁₂.₅₀D₄ = Q₈.₁₄D₆	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	4-	C12.50D4	96,158
C₁₂.₅₁D₄ = Dic₃⋊C₈	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	96		C12.51D4	96,21
C₁₂.₅₂D₄ = D₆⋊C₈	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48		C12.52D4	96,27
C₁₂.₅₃D₄ = C₁₂.₅₃D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	4	C12.53D4	96,29
C₁₂.₅₄D₄ = D₁₂⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	24	4	C12.54D4	96,32
C₁₂.₅₅D₄ = C₁₂.₅₅D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48		C12.55D4	96,37
C₁₂.₅₆D₄ = Q₈⋊₃Dic₃	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	24	4	C12.56D4	96,44
C₁₂.₅₇D₄ = Q₈.₁₃D₆	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	4	C12.57D4	96,157
C₁₂.₅₈D₄ = C₃×C₄.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	24	4	C12.58D4	96,50
C₁₂.₅₉D₄ = C₃×C₄.₁₀D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	4	C12.59D4	96,51
C₁₂.₆₀D₄ = C₃×D₄⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48		C12.60D4	96,52
C₁₂.₆₁D₄ = C₃×Q₈⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	96		C12.61D4	96,53
C₁₂.₆₂D₄ = C₃×C₂²⋊Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48		C12.62D4	96,169
C₁₂.₆₃D₄ = C₃×C₈⋊C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	24	4	C12.63D4	96,183
C₁₂.₆₄D₄ = C₃×C₈.C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₁₂	48	4	C12.64D4	96,184
C₁₂.₆₅D₄ = C₃×C₂²⋊C₈	central extension (φ=1)	48		C12.65D4	96,48
C₁₂.₆₆D₄ = C₃×C₄≀C₂	central extension (φ=1)	24	2	C12.66D4	96,54
C₁₂.₆₇D₄ = C₃×C₄⋊C₈	central extension (φ=1)	96		C12.67D4	96,55
C₁₂.₆₈D₄ = C₃×C₈.C₄	central extension (φ=1)	48	2	C12.68D4	96,58
C₁₂.₆₉D₄ = C₃×C₄○D₈	central extension (φ=1)	48	2	C12.69D4	96,182

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Extensions 1→N→G→Q→1 with N=C12 and Q=D4

Extensions 1→N→G→Q→1 with N=C₁₂ and Q=D₄