Subgroups — #2070⋊C₃ #68038

Order 384.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#338⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#2070	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	Q₈×A₄	—	4	1	no	maximal
4	#430	—	3	1	no	—
5	C₂×#101	—	3	1	no	—
6	#338	C₂×C₃	1	1	yes	characteristic
7	C₄×A₄	—	4	2	no	—
8	C₄×A₄	—	4	1	no	—
9	C₂²×Q₈	A₄	1	1	yes	characteristic
10	C₂×M₁₆	—	3	1	no	—
11	C₂×M₁₆	—	3	1	no	—
12	#108	—	6	2	no	—
13	#101	—	6	2	no	—
14	C₂×A₄	—	4	1	no	—
15	C₃×Q₈	—	16	1	no	—
16	C₂×Q₈	—	6	1	no	—
17	C₂×Q₈	—	6	1	no	—
18	C₂²×C₄	SL(2,𝔽₃)	1	2	yes	—
19	C₂²×C₄	C₂×A₄	1	1	yes	characteristic
20	M₁₆	—	3	2	no	—
21	M₁₆	—	6	1	no	—
22	M₁₆	—	6	1	no	—
23	M₁₆	—	6	1	no	—
24	C₂×C₈	—	6	1	no	—
25	C₂×C₈	—	6	1	no	—
26	A₄	—	4	1	no	—
27	C₃×C₄	—	16	2	no	—
28	C₃×C₄	—	16	1	no	—
29	C₂³	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
30	Q₈	—	4	1	no	—
31	Q₈	—	12	1	no	—
32	C₂×C₄	—	3	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	6	2	no	—
35	C₈	—	6	2	no	—
36	C₈	—	12	1	no	—
37	C₂×C₃	—	16	1	no	—
38	C₂²	—	3	1	no	—
39	C₂²	—	4	1	no	—
40	C₄	—	3	1	no	—
41	C₄	—	4	2	no	—
42	C₄	#126⋊C₃	1	1	yes	characteristic
43	C₃	—	16	1	no	Sylow
44	C₂	—	6	1	no	—
45	C₂	#396⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#396⋊C₃
commutator, cosocle, hypocenter	#338	C₂×C₃
Frattini	C₂²×C₄	C₂×A₄
Fitting	#2070	C₃
prime radical	#338⋊C₃	C₂
hypercenter	C₄	#126⋊C₃
LCS	G ▷ #338
UCS	C₁ ◁ C₂ ◁ C₄

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

N	H ≅ G/N	type
2. #2070	C₃	semidirect

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