Subgroups — #6235

Order 216.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#272	C₂	1	1	yes	maximal, characteristic, complemented
3	#1084	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#67	—	3	4	no	maximal
5	C₂×H(3,𝔽₃)	—	2	1	no	—
6	C₂×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
7	#272	—	2	1	no	—
8	C₂²×C₃²	D₃	1	4	yes	complemented
9	C₂×C₃×D₃	—	3	4	no	—
10	C₃×Dic₃	—	3	4	no	—
11	H(3,𝔽₃)	D₄	1	1	yes	characteristic, complemented, Sylow
12	C₃×D₄	—	9	1	no	—
13	#67	—	3	4	no	—
14	C₂×C₃²	—	2	4	no	—
15	C₂×C₃²	C₂×D₃	1	4	yes	—
16	C₃×D₃	—	6	4	no	—
17	C₂²×C₃	—	3	4	no	—
18	C₂²×C₃	—	9	1	no	—
19	C₂²×C₃	C₃⋊D₃	1	1	yes	characteristic
20	C₂×D₃	—	3	4	no	—
21	C₃×C₄	—	9	1	no	—
22	Dic₃	—	3	4	no	—
23	C₃²	#67	1	4	yes	complemented
24	D₄	—	9	1	no	Sylow
25	C₂×C₃	—	2	1	no	—
26	C₂×C₃	—	3	4	no	—
27	C₂×C₃	—	6	4	no	—
28	C₂×C₃	—	18	1	no	—
29	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
30	D₃	—	6	4	no	—
31	C₂²	—	9	1	no	—
32	C₂²	#272	1	1	yes	characteristic, complemented
33	C₄	—	9	1	no	—
34	C₃	—	3	4	no	—
35	C₃	#638	1	1	yes	characteristic
36	C₂	—	2	1	no	—
37	C₂	—	18	1	no	—
38	C₂	C₂×#272	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.