Subgroups — #63649

Order 288.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#3748	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#822	—	3	4	no	maximal
5	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₃²×C₈	—	2	1	no	—
7	C₃⋊(C₃⋊C₈)	—	2	1	no	—
8	C₃⋊(C₃⋊C₈)	C₄	1	2	yes	—
9	C₃×M₁₆	D₃	1	4	yes	—
10	#208	—	3	4	no	—
11	C₂×C₃⋊C₈	—	3	4	no	—
12	C₂²×C₃²	Q₈	1	1	yes	characteristic
13	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₃²×C₄	D₄	1	1	yes	characteristic
15	#108	—	9	1	no	Sylow
16	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
17	C₃×C₈	—	2	4	no	—
18	C₃⋊C₈	—	3	8	no	—
19	C₃⋊C₈	—	6	4	no	—
20	C₂×C₃²	—	2	1	no	—
21	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
22	M₁₆	—	9	1	no	—
23	M₁₆	C₃⋊D₃	1	1	yes	characteristic
24	C₂×C₈	—	9	1	no	—
25	C₂²×C₃	Dic₆	1	4	yes	—
26	C₃×C₄	C₄×D₃	1	4	yes	—
27	C₃×C₄	#67	1	4	yes	—
28	C₃²	#108	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
30	C₈	—	2	1	no	—
31	C₈	—	9	2	no	—
32	C₈	—	18	1	no	—
33	C₂×C₃	—	2	4	no	—
34	C₂×C₃	Dic₃⋊C₄	1	4	yes	—
35	C₂²	#634	1	1	yes	characteristic
36	C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
37	C₄	#638	1	1	yes	characteristic
38	C₃	#822	1	4	yes	complemented
39	C₂	—	2	1	no	—
40	C₂	#3750	1	1	yes	characteristic

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

N	H ≅ G/N	type
28. C₃²	#108	semidirect
38. C₃	#822	semidirect

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