Subgroups — #88589

Order 432.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6196	C₂	1	1	yes	maximal, characteristic
2	#6196	C₂	1	1	yes	maximal, characteristic
3	#6188	C₂	1	1	yes	maximal, characteristic
4	#1084	C₂²	1	1	yes	characteristic
5	(C₃⋊Dic₃)⋊C₃	—	2	1	no	—
6	(C₃⋊Dic₃)⋊C₃	—	2	1	no	—
7	#627	—	6	1	no	—
8	#627	—	6	1	no	—
9	C₂×H(3,𝔽₃)	D₄	1	1	yes	characteristic
10	Dic₁₂	—	9	1	no	maximal
11	C₃⋊Dic₃	—	2	1	no	—
12	C₃⋊Dic₃	—	2	1	no	—
13	C₃×Dic₃	—	6	1	no	—
14	C₃×Dic₃	—	6	1	no	—
15	C₃×Dic₃	—	6	1	no	—
16	C₃×Dic₃	—	6	1	no	—
17	H(3,𝔽₃)	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	Dic₆	—	9	1	no	—
19	Dic₆	—	9	1	no	—
20	Dic₆	—	18	1	no	—
21	Dic₆	—	18	1	no	—
22	C₃×C₈	—	9	1	no	—
23	C₂×C₃²	—	2	1	no	—
24	C₂×C₃²	—	2	1	no	—
25	Q₁₆	—	27	1	no	Sylow
26	C₃×C₄	—	9	1	no	—
27	C₃×C₄	—	18	1	no	—
28	C₃×C₄	—	18	1	no	—
29	Dic₃	—	6	1	no	—
30	Dic₃	—	6	1	no	—
31	Dic₃	—	6	1	no	—
32	Dic₃	—	6	1	no	—
33	Dic₃	—	18	1	no	—
34	Dic₃	—	36	1	no	—
35	C₃²	—	2	1	no	—
36	C₃²	—	2	1	no	—
37	Q₈	—	27	1	no	—
38	Q₈	—	27	1	no	—
39	C₈	—	9	1	no	—
40	C₂×C₃	—	6	1	no	—
41	C₂×C₃	—	12	1	no	—
42	C₂×C₃	GO⁺(4,𝔽₂)	1	1	yes	characteristic
43	C₄	—	9	1	no	—
44	C₄	—	18	1	no	—
45	C₄	—	18	1	no	—
46	C₃	—	6	1	no	—
47	C₃	—	12	1	no	—
48	C₃	#3776	1	1	yes	characteristic
49	C₂	#1088⋊C₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. H(3,𝔽₃)	Q₁₆	semidirect

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