Subgroups — H(3,𝔽₃)⋊C₉ #6870

Order 243.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃³	—	3	1	no	—
5	C₃³	C₃²	1	1	yes	characteristic
6	H(3,𝔽₃)	—	3	2	no	—
7	H(3,𝔽₃)	C₉	1	3	yes	complemented
8	C₃×C₉	—	3	1	no	—
9	C₃×C₉	—	3	3	no	—
10	C₃×C₉	—	3	2	no	—
11	C₃²	—	3	1	no	—
12	C₃²	—	3	1	no	—
13	C₃²	—	3	1	no	—
14	C₃²	—	3	3	no	—
15	C₃²	—	9	1	no	—
16	C₃²	—	9	1	no	—
17	C₃²	—	9	1	no	—
18	C₃²	C₃×C₉	1	1	yes	characteristic
19	C₃²	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²	3₋¹⁺²	1	2	yes	—
21	C₉	—	3	3	no	—
22	C₉	—	9	2	no	—
23	C₃	—	3	1	no	—
24	C₃	—	3	2	no	—
25	C₃	—	9	3	no	—
26	C₃	C₃²⋊C₉	1	1	yes	characteristic
27	C₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
28	C₃	#731	1	1	yes	characteristic
29	C₃	#732	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.