Subgroups — C₂₄₃⋊C₈ #14515607

Order 1944.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₄₃	C₂	1	1	yes	maximal, characteristic
2	C₈₁⋊C₈	—	3	1	no	maximal
3	C₂×C₂₄₃	C₄	1	1	yes	characteristic
4	C₄×C₈₁	D₃	1	1	yes	characteristic
5	C₂₄₃	C₈	1	1	yes	characteristic, complemented, Sylow
6	C₂₇⋊C₈	—	9	1	no	—
7	C₂×C₈₁	Dic₃	1	1	yes	characteristic
8	C₄×C₂₇	D₉	1	1	yes	characteristic
9	C₈₁	C₃⋊C₈	1	1	yes	characteristic
10	C₉⋊C₈	—	27	1	no	—
11	C₂×C₂₇	Dic₉	1	1	yes	characteristic
12	C₄×C₉	D₂₇	1	1	yes	characteristic
13	C₂₇	C₉⋊C₈	1	1	yes	characteristic
14	C₃⋊C₈	—	81	1	no	—
15	C₂×C₉	Dic₂₇	1	1	yes	characteristic
16	C₃×C₄	D₈₁	1	1	yes	characteristic
17	C₉	C₂₇⋊C₈	1	1	yes	characteristic
18	C₈	—	243	1	no	Sylow
19	C₂×C₃	Dic₈₁	1	1	yes	characteristic
20	C₄	D₂₄₃	1	1	yes	characteristic
21	C₃	C₈₁⋊C₈	1	1	yes	characteristic
22	C₂	Dic₂₄₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₂₄₃	C₈	semidirect

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

subgroup	index
C₄×C₂₄₃	2
C₈₁⋊C₈	3