Subgroups — C₂×D₉⋊C₉ #66372

Order 324.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₉	—	3	1	no	maximal
4	C₂×C₃×D₉	C₃	1	1	yes	maximal, characteristic
5	C₉⋊C₉	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃×C₉	—	2	1	no	—
7	C₂×C₃×C₉	D₃	1	1	yes	characteristic
8	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
9	D₃×C₉	—	3	2	no	—
10	C₃×D₉	C₂×C₃	1	2	yes	—
11	C₂×C₃×D₃	—	3	1	no	—
12	C₂²×C₉	—	9	1	no	—
13	C₂×D₉	C₉	1	1	yes	characteristic, complemented
14	C₃×C₉	—	2	1	no	—
15	C₃×C₉	C₂×D₃	1	1	yes	characteristic
16	C₃×C₉	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₃²	C₃×D₃	1	1	yes	characteristic
18	C₃×D₃	—	3	2	no	—
19	C₂×C₉	—	2	1	no	—
20	C₂×C₉	—	3	1	no	—
21	C₂×C₉	—	6	1	no	—
22	C₂×C₉	—	9	2	no	—
23	C₂×C₉	C₂×C₉	1	1	yes	characteristic, complemented
24	D₉	C₂×C₉	1	2	yes	complemented
25	C₂²×C₃	—	9	1	no	—
26	C₂×D₃	—	3	1	no	—
27	C₃²	C₂×C₃×D₃	1	1	yes	characteristic
28	C₉	—	2	1	no	—
29	C₉	—	3	1	no	—
30	C₉	—	6	1	no	—
31	C₉	C₂²×C₉	1	1	yes	characteristic, complemented
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	—	9	2	no	—
34	C₂×C₃	D₃×C₉	1	1	yes	characteristic
35	C₂×C₃	AGL(1,ℤ/9)	1	1	yes	characteristic
36	D₃	—	3	2	no	—
37	C₂²	—	9	1	no	Sylow
38	C₃	—	2	1	no	—
39	C₃	C₂×D₃×C₉	1	1	yes	characteristic
40	C₃	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
41	C₂	—	9	2	no	—
42	C₂	D₉⋊C₉	1	1	yes	characteristic, direct product factor

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.