Subgroups — C₉×#226 #88593

Order 432.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃×#226	C₃	1	1	yes	maximal, characteristic
3	C₉×Q₁₆	—	3	1	no	maximal
4	C₉×Dic₃	—	4	1	no	maximal
5	C₃×SL(2,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	Q₈×C₉	—	3	1	no	—
7	Q₈×C₉	D₃	1	1	yes	characteristic
8	Q₈⋊C₉	—	2	1	no	—
9	C₈×C₉	—	3	1	no	—
10	C₂×C₃×C₉	—	4	1	no	—
11	#226	C₉	1	1	yes	characteristic, direct product factor
12	C₃×Q₁₆	—	3	1	no	—
13	C₃×Dic₃	—	4	1	no	—
14	C₄×C₉	—	3	1	no	—
15	C₄×C₉	—	6	1	no	—
16	C₃×C₉	—	4	1	no	Sylow
17	C₃×Q₈	—	3	1	no	—
18	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
19	SL(2,𝔽₃)	—	2	1	no	—
20	SL(2,𝔽₃)	C₂×C₉	1	1	yes	characteristic
21	C₃×C₈	—	3	1	no	—
22	C₂×C₃²	—	4	1	no	—
23	C₂×C₉	—	8	1	no	—
24	C₂×C₉	S₄	1	1	yes	characteristic
25	Q₁₆	—	3	1	no	Sylow
26	C₃×C₄	—	3	1	no	—
27	C₃×C₄	—	6	1	no	—
28	Dic₃	—	4	1	no	—
29	C₃²	—	4	1	no	—
30	C₉	—	8	1	no	—
31	C₉	#226	1	1	yes	characteristic, direct product factor
32	Q₈	—	3	1	no	—
33	Q₈	D₃×C₉	1	1	yes	characteristic
34	C₈	—	3	1	no	—
35	C₂×C₃	—	4	1	no	—
36	C₂×C₃	—	8	1	no	—
37	C₂×C₃	C₃×S₄	1	1	yes	characteristic
38	C₄	—	3	1	no	—
39	C₄	—	6	1	no	—
40	C₃	—	4	1	no	—
41	C₃	—	8	1	no	—
42	C₃	C₃×#226	1	1	yes	characteristic
43	C₂	C₉×S₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. #226	C₉	direct (N × H)
31. C₉	#226	direct (N × H)

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