Subgroups — #88627

Order 432.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#272	C₂	1	1	yes	maximal, characteristic
2	#6188	C₂	1	2	yes	maximal, complemented
3	C₂×#272	C₄	1	1	yes	characteristic
4	C₄×H(3,𝔽₃)	C₄	1	1	yes	characteristic
5	#1084	C₂²	1	1	yes	characteristic
6	C₃×C₄×D₃	—	6	2	no	—
7	C₂×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
8	#272	—	2	1	no	—
9	C₃×M₁₆	—	9	1	no	maximal
10	C₂×C₃×D₃	—	6	2	no	—
11	C₃²×C₄	—	2	2	no	—
12	C₃×Dic₃	—	6	2	no	—
13	H(3,𝔽₃)	M₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₃×C₄	—	9	1	no	—
15	C₄×D₃	—	6	2	no	—
16	C₃×C₈	—	9	2	no	—
17	C₂×C₃²	—	2	2	no	—
18	C₃×D₃	—	6	4	no	—
19	M₁₆	—	9	1	no	Sylow
20	C₂²×C₃	—	9	1	no	—
21	C₂×D₃	—	6	2	no	—
22	C₃×C₄	—	9	1	no	—
23	C₃×C₄	—	12	2	no	—
24	C₃×C₄	#157	1	1	yes	characteristic
25	Dic₃	—	6	2	no	—
26	C₃²	—	2	2	no	—
27	C₂×C₄	—	9	1	no	—
28	C₈	—	9	2	no	—
29	C₂×C₃	—	12	2	no	—
30	C₂×C₃	—	18	1	no	—
31	C₂×C₃	C₂×#157	1	1	yes	characteristic
32	D₃	—	6	4	no	—
33	C₂²	—	9	1	no	—
34	C₄	—	9	1	no	—
35	C₄	#1088	1	1	yes	characteristic
36	C₃	—	12	2	no	—
37	C₃	#3788	1	1	yes	characteristic
38	C₂	—	18	1	no	—
39	C₂	C₂×#1088	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #6188	C₂	semidirect
13. H(3,𝔽₃)	M₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.