Subgroups — C₃×C₃²⋊C₉ #6885

Order 243.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₉	C₃	1	3	yes	maximal, complemented
3	C₃²⋊C₉	C₃	1	9	yes	maximal, direct product factor
4	C₃³	—	3	3	no	—
5	C₃³	—	3	6	no	—
6	C₃³	C₉	1	9	yes	complemented
7	C₃³	C₃²	1	3	yes	—
8	C₃³	C₃²	1	1	yes	characteristic
9	C₃×C₉	—	3	9	no	—
10	C₃×C₉	C₃²	1	9	yes	complemented
11	C₃²	—	3	27	no	—
12	C₃²	—	3	3	no	—
13	C₃²	—	3	6	no	—
14	C₃²	C₃×C₉	1	3	yes	—
15	C₃²	C₃×C₉	1	9	yes	complemented
16	C₃²	H(3,𝔽₃)	1	3	yes	—
17	C₃²	3₋¹⁺²	1	6	yes	—
18	C₃²	C₃³	1	1	yes	characteristic
19	C₉	—	3	9	no	—
20	C₃	—	3	9	no	—
21	C₃	C₃²⋊C₉	1	9	yes	direct product factor
22	C₃	C₃²×C₉	1	1	yes	characteristic
23	C₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
24	C₃	C₃×3₋¹⁺²	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.