Subgroups — (C₂²⋊C₉)⋊C₉ #66355

Order 324.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊C₉	C₃	1	2	yes	maximal
3	C₃×C₂²⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₉⋊C₉	—	4	1	no	maximal, Sylow
5	C₂×C₃×C₉	—	3	1	no	—
6	C₂²×C₃²	C₃²	1	1	yes	characteristic
7	C₂²×C₉	—	3	1	no	—
8	C₂²⋊C₉	—	3	2	no	—
9	C₂²⋊C₉	C₉	1	3	yes	complemented
10	C₃×C₉	—	4	1	no	—
11	C₃×C₉	—	4	2	no	—
12	C₃×C₉	A₄	1	1	yes	characteristic
13	C₂×C₃²	—	3	1	no	—
14	C₂×C₉	—	3	3	no	—
15	C₂²×C₃	C₃×C₉	1	1	yes	characteristic
16	C₂²×C₃	3₋¹⁺²	1	2	yes	—
17	C₂²×C₃	3₋¹⁺²	1	1	yes	characteristic
18	C₃²	C₃×A₄	1	1	yes	characteristic
19	C₉	—	3	1	no	—
20	C₉	—	4	3	no	—
21	C₉	—	12	2	no	—
22	C₂×C₃	—	3	1	no	—
23	C₂×C₃	—	3	2	no	—
24	C₂×C₃	—	3	1	no	—
25	C₂²	C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
26	C₃	C₉×A₄	1	1	yes	characteristic
27	C₃	C₉⋊A₄	1	2	yes	—
28	C₃	#1094	1	1	yes	characteristic
29	C₂	—	3	1	no	—

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

N	H ≅ G/N	type
9. C₂²⋊C₉	C₉	semidirect
25. C₂²	C₉⋊C₉	semidirect

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