Subgroups — #6189

Order 216.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊Dic₉	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃×Dic₉	C₂	1	1	yes	maximal, characteristic
4	#627	—	3	1	no	maximal
5	Dic₁₈	—	3	1	no	maximal
6	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃	—	3	1	no	—
8	C₃×Dic₃	—	3	1	no	—
9	C₃×Dic₃	D₃	1	1	yes	characteristic
10	C₄×C₉	—	3	1	no	—
11	Dic₉	—	3	1	no	—
12	Dic₉	—	6	1	no	—
13	Dic₉	D₃	1	1	yes	characteristic
14	C₃×C₉	Q₈	1	1	yes	characteristic, complemented, Sylow
15	Dic₆	—	9	1	no	—
16	Dic₆	—	9	1	no	—
17	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
18	C₂×C₉	—	2	1	no	—
19	C₂×C₉	C₂×D₃	1	1	yes	characteristic
20	C₃×C₄	—	3	1	no	—
21	C₃×C₄	—	9	1	no	—
22	Dic₃	—	3	1	no	—
23	Dic₃	—	9	1	no	—
24	Dic₃	—	9	1	no	—
25	Dic₃	—	18	1	no	—
26	Dic₃	D₉	1	1	yes	characteristic
27	C₃²	Dic₆	1	1	yes	characteristic
28	C₉	—	2	1	no	—
29	C₉	Dic₆	1	1	yes	characteristic, complemented
30	Q₈	—	27	1	no	Sylow
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	C₂×D₉	1	1	yes	characteristic
33	C₂×C₃	D₃²	1	1	yes	characteristic
34	C₄	—	3	1	no	—
35	C₄	—	9	1	no	—
36	C₄	—	27	1	no	—
37	C₃	—	2	1	no	—
38	C₃	Dic₁₈	1	1	yes	characteristic, complemented
39	C₃	#627	1	1	yes	characteristic
40	C₂	D₃×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.