Subgroups — C₉×H(3,𝔽₃) #6888

Order 243.

101 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	4	yes	maximal, complemented
3	C₃²⋊C₉	C₃	1	8	yes	maximal, complemented
4	C₃³	C₃²	1	4	yes	—
5	H(3,𝔽₃)	C₉	1	9	yes	direct product factor
6	C₃×C₉	—	3	12	no	—
7	C₃×C₉	C₃²	1	8	yes	—
8	C₃×C₉	C₃²	1	1	yes	characteristic
9	C₃²	—	3	4	no	—
10	C₃²	—	3	8	no	—
11	C₃²	C₃×C₉	1	12	yes	complemented
12	C₃²	C₃³	1	1	yes	characteristic
13	C₉	—	3	8	no	—
14	C₉	H(3,𝔽₃)	1	3	yes	direct product factor
15	C₃	—	3	12	no	—
16	C₃	C₃²×C₉	1	1	yes	characteristic
17	C₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
18	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.