Subgroups — #6199

Order 216.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#272	C₂	1	1	yes	maximal, characteristic
2	(C₃⋊Dic₃)⋊C₃	C₂	1	2	yes	maximal, complemented
3	D₃×Dic₃	—	3	2	no	maximal
4	C₂×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
5	#272	C₄	1	2	yes	complemented
6	C₂×C₃×D₃	—	3	2	no	—
7	C₂×C₃×D₃	—	6	1	no	—
8	C₃⋊Dic₃	D₃	1	2	yes	complemented
9	C₃×Dic₃	—	3	2	no	—
10	H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂×Dic₃	—	9	1	no	—
12	C₄×D₃	—	9	2	no	—
13	C₂×C₃²	—	2	1	no	—
14	C₂×C₃²	C₂×D₃	1	2	yes	—
15	C₃×D₃	—	3	4	no	—
16	C₃×D₃	—	6	2	no	—
17	C₂²×C₃	—	9	1	no	—
18	C₂×D₃	—	3	2	no	—
19	C₂×D₃	—	6	1	no	—
20	C₃×C₄	—	9	2	no	—
21	Dic₃	—	3	2	no	—
22	Dic₃	—	9	2	no	—
23	C₃²	—	2	1	no	—
24	C₃²	C₄×D₃	1	2	yes	complemented
25	C₂×C₄	—	27	1	no	Sylow
26	C₂×C₃	—	3	2	no	—
27	C₂×C₃	—	6	1	no	—
28	C₂×C₃	—	9	2	no	—
29	C₂×C₃	D₃²	1	1	yes	characteristic
30	D₃	—	3	4	no	—
31	D₃	—	6	2	no	—
32	C₂²	—	9	1	no	—
33	C₄	—	9	2	no	—
34	C₃	—	3	2	no	—
35	C₃	—	6	1	no	—
36	C₃	#624	1	1	yes	characteristic
37	C₂	—	9	2	no	—
38	C₂	((C₃⋊D₃)⋊C₃)⋊C₂	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.