Subgroups — C₃×#1368 #67928

Order 384.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#346	C₂	1	1	yes	maximal, characteristic
2	C₃×#334	C₂	1	2	yes	maximal
3	#1368	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₃×C₁₆	C₄	1	1	yes	characteristic
6	C₃×C₄⋊C₈	—	2	2	no	—
7	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
8	#346	C₂×C₃	1	1	yes	characteristic
9	#334	C₂×C₃	1	2	yes	—
10	C₂×C₃×C₈	—	4	2	no	—
11	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₈	Q₈	1	1	yes	characteristic
13	C₃×C₄²	D₄	1	1	yes	characteristic
14	C₃×C₁₆	—	2	1	no	—
15	C₃×C₁₆	C₈	1	2	yes	complemented
16	C₂×C₁₆	C₃×C₄	1	1	yes	characteristic
17	C₂×C₁₆	C₃×C₄	1	1	yes	characteristic
18	C₄⋊C₈	—	2	2	no	—
19	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃×C₄	SD₁₆	1	2	yes	—
22	C₃×C₈	—	2	1	no	—
23	C₃×C₈	—	8	2	no	—
24	C₃×C₈	C₂×C₈	1	1	yes	characteristic
25	C₃×C₈	M₁₆	1	1	yes	characteristic
26	C₂×C₈	—	4	2	no	—
27	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
28	C₂×C₈	C₃×Q₈	1	1	yes	characteristic
29	C₄²	C₃×D₄	1	1	yes	characteristic
30	C₁₆	—	2	1	no	—
31	C₁₆	C₃×C₈	1	2	yes	complemented
32	C₂²×C₃	#106	1	1	yes	characteristic
33	C₃×C₄	—	2	2	no	—
34	C₃×C₄	C₄⋊C₈	1	1	yes	characteristic
35	C₃×C₄	#108	1	1	yes	characteristic
36	C₂×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄	C₃×SD₁₆	1	2	yes	—
38	C₈	—	2	1	no	—
39	C₈	—	8	2	no	—
40	C₈	C₂×C₃×C₈	1	1	yes	characteristic
41	C₈	C₃×M₁₆	1	1	yes	characteristic
42	C₂×C₃	#334	1	1	yes	characteristic
43	C₂×C₃	#365	1	2	yes	—
44	C₂²	C₃×#106	1	1	yes	characteristic
45	C₄	—	2	2	no	—
46	C₄	C₃×C₄⋊C₈	1	1	yes	characteristic
47	C₄	C₃×#108	1	1	yes	characteristic
48	C₃	#1368	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	C₃×#334	1	1	yes	characteristic
50	C₂	C₃×#365	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	#106
commutator	C₈	C₂×C₃×C₈
Frattini, cosocle	C₄×C₈	C₂²×C₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1368	C₃	direct (N × H)
15. C₃×C₁₆	C₈	semidirect
31. C₁₆	C₃×C₈	semidirect
48. C₃	#1368	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#346	2
C₃×#334	2
#1368	3

Subgroups — C3×#1368 #67928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1368 #67928