Subgroups — C₃×#131⋊C₃ #63990

Order 288.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#131	C₃	1	1	yes	maximal, characteristic, complemented
3	#131⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
5	C₃²×C₈	—	4	1	no	maximal
6	C₃×#41	C₂×C₃	1	1	yes	characteristic
7	#41⋊C₃	C₂×C₃	1	3	yes	—
8	C₃×M₁₆	—	3	1	no	—
9	C₂×C₃×C₈	—	3	1	no	—
10	C₃²×C₄	—	4	1	no	—
11	#131	C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₃×Q₈	C₃×C₄	1	1	yes	characteristic
13	C₃×D₄	—	3	1	no	—
14	C₂×C₃×C₄	—	3	1	no	—
15	SL(2,𝔽₃)	C₃×C₄	1	3	yes	—
16	C₃×C₈	—	3	1	no	—
17	C₃×C₈	—	4	3	no	—
18	C₃×C₈	A₄	1	1	yes	characteristic
19	C₂×C₃²	—	4	1	no	—
20	#41	C₂×C₃²	1	1	yes	characteristic
21	M₁₆	—	3	1	no	—
22	C₂×C₈	—	3	1	no	—
23	C₂²×C₃	—	3	1	no	—
24	C₃×C₄	—	3	1	no	—
25	C₃×C₄	—	4	3	no	—
26	C₃×C₄	C₂×A₄	1	1	yes	characteristic
27	C₃²	—	4	1	no	Sylow
28	Q₈	C₃²×C₄	1	1	yes	characteristic
29	D₄	—	3	1	no	—
30	C₂×C₄	—	3	1	no	—
31	C₈	—	3	1	no	—
32	C₈	C₃×A₄	1	1	yes	characteristic
33	C₂×C₃	—	4	3	no	—
34	C₂×C₃	—	6	1	no	—
35	C₂×C₃	C₄×A₄	1	1	yes	characteristic
36	C₂²	—	3	1	no	—
37	C₄	—	3	1	no	—
38	C₄	C₂×C₃×A₄	1	1	yes	characteristic
39	C₃	—	4	3	no	—
40	C₃	#131⋊C₃	1	1	yes	characteristic, direct product factor
41	C₂	—	6	1	no	—
42	C₂	C₃×C₄×A₄	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.