Subgroups — #88433

Order 432.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#634⋊C₃	C₂	1	2	yes	maximal
2	#6180	C₂	1	1	yes	maximal, characteristic
3	#3719	—	3	2	no	maximal
4	C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
5	(C₃⋊Dic₃)⋊C₃	—	2	2	no	—
6	#634	D₃	1	2	yes	—
7	C₃×Dic₆	—	3	2	no	—
8	C₃×C₃⋊C₈	—	3	2	no	—
9	C₃×C₃⋊C₈	—	6	1	no	—
10	C₂×H(3,𝔽₃)	D₄	1	1	yes	characteristic
11	#216	—	9	2	no	—
12	Dic₁₂	—	9	1	no	—
13	C₃²×C₄	—	2	1	no	—
14	C₃²×C₄	C₂×D₃	1	2	yes	—
15	C₃⋊Dic₃	—	2	2	no	—
16	C₃×Dic₃	—	6	2	no	—
17	H(3,𝔽₃)	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₃×Q₈	—	9	2	no	—
19	Dic₆	—	3	2	no	—
20	Dic₆	—	18	2	no	—
21	C₃×C₈	—	9	1	no	—
22	C₃⋊C₈	—	3	2	no	—
23	C₃⋊C₈	—	6	1	no	—
24	C₂×C₃²	—	2	1	no	—
25	C₂×C₃²	#67	1	2	yes	—
26	Q₁₆	—	27	1	no	Sylow
27	C₃×C₄	—	6	2	no	—
28	C₃×C₄	—	12	1	no	—
29	C₃×C₄	—	18	2	no	—
30	C₃×C₄	D₃²	1	1	yes	characteristic
31	Dic₃	—	6	2	no	—
32	Dic₃	—	18	2	no	—
33	C₃²	—	2	1	no	—
34	C₃²	#216	1	2	yes	complemented
35	Q₈	—	9	2	no	—
36	C₈	—	9	1	no	—
37	C₂×C₃	—	6	2	no	—
38	C₂×C₃	—	12	1	no	—
39	C₂×C₃	#625	1	1	yes	characteristic
40	C₄	—	18	2	no	—
41	C₄	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
42	C₃	—	6	2	no	—
43	C₃	—	12	1	no	—
44	C₃	#3718	1	1	yes	characteristic
45	C₂	#6198	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
34. C₃²	#216	semidirect

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