Subgroups — #6233

Order 216.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#638	—	3	1	no	maximal
5	#611	—	3	3	no	maximal
6	C₂×C₃×C₉	—	2	1	no	—
7	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
8	C₃⋊D₉	—	2	1	no	—
9	C₂²×C₃²	D₃	1	1	yes	characteristic
10	C₂×C₃⋊D₃	—	3	1	no	—
11	C₃⋊Dic₃	—	3	1	no	—
12	C₂²×C₉	D₃	1	3	yes	complemented
13	C₂×D₉	—	3	3	no	—
14	Dic₉	—	3	3	no	—
15	C₃×C₉	D₄	1	1	yes	characteristic, complemented, Sylow
16	#67	—	9	3	no	—
17	#67	—	9	1	no	—
18	C₂×C₃²	—	2	1	no	—
19	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
20	C₃⋊D₃	—	6	1	no	—
21	C₂×C₉	—	2	3	no	—
22	C₂×C₉	C₂×D₃	1	3	yes	—
23	D₉	—	6	3	no	—
24	C₂²×C₃	D₉	1	3	yes	complemented
25	C₂²×C₃	C₃⋊D₃	1	1	yes	characteristic
26	C₂×D₃	—	9	3	no	—
27	C₂×D₃	—	9	1	no	—
28	Dic₃	—	9	3	no	—
29	Dic₃	—	9	1	no	—
30	C₃²	#67	1	1	yes	characteristic
31	C₉	#67	1	3	yes	complemented
32	D₄	—	27	1	no	Sylow
33	C₂×C₃	—	2	3	no	—
34	C₂×C₃	—	2	1	no	—
35	C₂×C₃	C₂×D₉	1	3	yes	—
36	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
37	D₃	—	18	3	no	—
38	D₃	—	18	1	no	—
39	C₂²	—	27	1	no	—
40	C₂²	C₃⋊D₉	1	1	yes	characteristic, complemented
41	C₄	—	27	1	no	—
42	C₃	#611	1	3	yes	complemented
43	C₃	#638	1	1	yes	characteristic
44	C₂	—	2	1	no	—
45	C₂	—	54	1	no	—
46	C₂	C₂×C₃⋊D₉	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.