Subgroups — C₉⋊C₂₄₃ #14546523

Order 2187.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₄₃	C₃	1	3	yes	maximal
2	C₉×C₈₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₈₁	C₉	1	2	yes	—
4	C₃×C₈₁	C₃²	1	1	yes	characteristic
5	C₉×C₂₇	C₉	1	1	yes	characteristic
6	C₂₄₃	—	3	3	no	—
7	C₃×C₂₇	C₂₇	1	2	yes	—
8	C₃×C₂₇	C₃×C₉	1	1	yes	characteristic
9	C₉²	C₂₇	1	1	yes	characteristic
10	C₈₁	—	3	2	no	—
11	C₈₁	3₋¹⁺²	1	3	yes	—
12	C₃×C₉	C₈₁	1	2	yes	—
13	C₃×C₉	C₈₁	1	1	yes	characteristic
14	C₃×C₉	C₃×C₂₇	1	1	yes	characteristic
15	C₂₇	—	3	2	no	—
16	C₂₇	C₉⋊C₉	1	1	yes	characteristic
17	C₂₇	C₂₇⋊C₃	1	2	yes	—
18	C₃²	C₃×C₈₁	1	1	yes	characteristic
19	C₉	—	3	2	no	—
20	C₉	C₂₄₃	1	3	yes	complemented
21	C₉	C₉⋊C₂₇	1	1	yes	characteristic
22	C₉	C₈₁⋊C₃	1	2	yes	—
23	C₃	C₉⋊C₈₁	1	1	yes	characteristic
24	C₃	C₃×C₂₄₃	1	1	yes	characteristic
25	C₃	C₂₄₃⋊C₃	1	2	yes	—

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

N	H ≅ G/N	type
20. C₉	C₂₄₃	semidirect

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

subgroup	index
C₃×C₂₄₃	3
C₉×C₈₁	3