Subgroups — C₄×#272 #6230

Order 216.

88 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	C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#1084	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₃	—	3	4	no	maximal
5	C₂×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
6	#272	C₄	1	2	yes	direct product factor
7	C₂×C₃×D₃	—	3	4	no	—
8	C₃²×C₄	D₃	1	4	yes	complemented
9	C₃×Dic₃	—	3	4	no	—
10	H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₃×C₄	—	9	1	no	—
12	C₄×D₃	—	3	4	no	—
13	C₂×C₃²	C₂×D₃	1	4	yes	—
14	C₃×D₃	—	3	8	no	—
15	C₂²×C₃	—	9	1	no	—
16	C₂×D₃	—	3	4	no	—
17	C₃×C₄	—	3	4	no	—
18	C₃×C₄	—	9	1	no	—
19	C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
20	Dic₃	—	3	4	no	—
21	C₃²	C₄×D₃	1	4	yes	complemented
22	C₂×C₄	—	9	1	no	Sylow
23	C₂×C₃	—	3	4	no	—
24	C₂×C₃	—	9	2	no	—
25	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
26	D₃	—	3	8	no	—
27	C₂²	—	9	1	no	—
28	C₄	—	9	1	no	—
29	C₄	#272	1	1	yes	characteristic, direct product factor
30	C₃	—	3	4	no	—
31	C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
32	C₂	—	9	2	no	—
33	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.