Subgroups — #88626

Order 432.

65 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	1	no	—
7	C₃×C₄×D₃	—	6	1	no	—
8	C₂×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
9	#272	C₈	1	2	yes	complemented
10	C₂×C₃×C₈	—	9	1	no	maximal
11	C₂×C₃×D₃	—	6	1	no	—
12	C₂×C₃×D₃	—	6	1	no	—
13	C₃²×C₄	—	2	1	no	—
14	C₃²×C₄	—	2	1	no	—
15	C₃×Dic₃	—	6	1	no	—
16	C₃×Dic₃	—	6	1	no	—
17	H(3,𝔽₃)	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₄	—	9	1	no	—
19	C₄×D₃	—	6	1	no	—
20	C₄×D₃	—	6	1	no	—
21	C₃×C₈	—	9	2	no	—
22	C₂×C₃²	—	2	1	no	—
23	C₂×C₃²	—	2	1	no	—
24	C₃×D₃	—	6	2	no	—
25	C₃×D₃	—	6	2	no	—
26	C₂×C₈	—	9	1	no	Sylow
27	C₂²×C₃	—	9	1	no	—
28	C₂×D₃	—	6	1	no	—
29	C₂×D₃	—	6	1	no	—
30	C₃×C₄	—	6	1	no	—
31	C₃×C₄	—	9	1	no	—
32	C₃×C₄	—	12	1	no	—
33	C₃×C₄	#157	1	1	yes	characteristic
34	Dic₃	—	6	1	no	—
35	Dic₃	—	6	1	no	—
36	C₃²	—	2	1	no	—
37	C₃²	—	2	1	no	—
38	C₂×C₄	—	9	1	no	—
39	C₈	—	9	2	no	—
40	C₂×C₃	—	6	1	no	—
41	C₂×C₃	—	9	2	no	—
42	C₂×C₃	—	12	1	no	—
43	C₂×C₃	C₂×#157	1	1	yes	characteristic
44	D₃	—	6	2	no	—
45	D₃	—	6	2	no	—
46	C₂²	—	9	1	no	—
47	C₄	—	9	1	no	—
48	C₄	#1088	1	1	yes	characteristic
49	C₃	—	6	1	no	—
50	C₃	—	12	1	no	—
51	C₃	#3787	1	1	yes	characteristic
52	C₂	—	9	2	no	—
53	C₂	C₂×#1088	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.