Subgroups — #2845⋊C₃ #73295

Order 384.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2845	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂×C₄²⋊C₃	—	4	1	no	maximal
3	#95⋊C₃	—	4	4	no	maximal
4	#398	—	3	4	no	—
5	#382	—	3	1	no	—
6	C₄²⋊C₃	—	4	1	no	—
7	C₂×C₄⋊C₄	—	3	2	no	—
8	C₂×C₄⋊C₄	—	3	4	no	—
9	C₂×C₄²	A₄	1	1	yes	characteristic
10	#95	—	3	4	no	—
11	#95	A₄	1	4	yes	—
12	C₂×A₄	—	16	1	no	—
13	C₂²×C₄	—	3	1	no	—
14	C₂²×C₄	—	3	4	no	—
15	C₄⋊C₄	—	12	2	no	—
16	C₄⋊C₄	—	12	4	no	—
17	C₄²	—	3	1	no	—
18	C₄²	SL(2,𝔽₃)	1	1	yes	characteristic
19	A₄	—	16	1	no	—
20	C₂³	C₂²⋊A₄	1	1	yes	characteristic
21	C₂×C₄	—	3	1	no	—
22	C₂×C₄	—	3	1	no	—
23	C₂×C₄	—	6	1	no	—
24	C₂×C₄	—	6	1	no	—
25	C₂×C₄	—	6	4	no	—
26	C₂×C₄	—	6	4	no	—
27	C₂×C₄	—	6	4	no	—
28	C₂×C₃	—	64	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	—	3	1	no	—
31	C₂²	C₂²⋊SL(2,𝔽₃)	1	1	yes	characteristic
32	C₄	—	6	1	no	—
33	C₄	—	6	1	no	—
34	C₄	—	12	4	no	—
35	C₃	—	64	1	no	Sylow
36	C₂	—	3	1	no	—
37	C₂	—	3	1	no	—
38	C₂	#564⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#564⋊C₃
commutator, Fitting, cosocle, hypocenter	#2845	C₃
Frattini, socle	C₂³	C₂²⋊A₄
LCS	G ▷ #2845
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
1. #2845	C₃	semidirect

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