Subgroups — C₉×3₋¹⁺² #6889

Order 243.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₉	C₃	1	1	yes	maximal, characteristic
3	C₉⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃²⋊C₉	C₃	1	2	yes	maximal
5	C₉²	C₃	1	3	yes	maximal, complemented
6	C₃³	C₃²	1	1	yes	characteristic
7	3₋¹⁺²	C₉	1	9	yes	direct product factor
8	C₃×C₉	—	3	3	no	—
9	C₃×C₉	C₃²	1	6	yes	—
10	C₃×C₉	C₃²	1	2	yes	—
11	C₃×C₉	C₃²	1	3	yes	—
12	C₃×C₉	C₃²	1	1	yes	characteristic
13	C₃²	—	3	1	no	—
14	C₃²	—	3	2	no	—
15	C₃²	C₃×C₉	1	3	yes	—
16	C₃²	C₃³	1	1	yes	characteristic
17	C₉	—	3	2	no	—
18	C₉	—	3	6	no	—
19	C₉	C₃×C₉	1	9	yes	complemented
20	C₉	3₋¹⁺²	1	3	yes	direct product factor
21	C₃	—	3	3	no	—
22	C₃	C₃²×C₉	1	1	yes	characteristic
23	C₃	C₃×3₋¹⁺²	1	1	yes	characteristic
24	C₃	#737	1	2	yes	—

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.