Subgroups — C₄×Dic₁₂₁₃ #34085113

Order 19408.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₁₃	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₂₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₂₁₃	C₂²	1	1	yes	characteristic
4	C₄×C₁₂₁₃	C₄	1	2	yes	complemented
5	Dic₁₂₁₃	C₄	1	4	yes	direct product factor
6	C₂×C₁₂₁₃	C₂×C₄	1	2	yes	—
7	C₂×C₁₂₁₃	C₂×C₄	1	1	yes	characteristic
8	C₁₂₁₃	C₄²	1	1	yes	characteristic, complemented, Sylow
9	C₄²	—	1213	1	no	maximal, Sylow
10	C₂×C₄	—	1213	2	no	—
11	C₂×C₄	D₁₂₁₃	1	1	yes	characteristic
12	C₂²	C₂×D₁₂₁₃	1	1	yes	characteristic
13	C₄	—	1213	4	no	—
14	C₄	Dic₁₂₁₃	1	2	yes	direct product factor
15	C₂	C₄×D₁₂₁₃	1	2	yes	—
16	C₂	C₂×Dic₁₂₁₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.