Subgroups — C₂×C₃×#6862 #13090072

Order 1458.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6862	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×C₃²⋊C₉	C₃	1	4	yes	maximal
3	C₂×#6862	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₃²⋊C₉	C₂×C₃	1	4	yes	—
5	#6862	C₂×C₃	1	9	yes	direct product factor
6	C₂×C₃⁴	C₃²	1	1	yes	characteristic
7	C₂×C₃²×C₉	—	3	4	no	—
8	C₂×C₃²⋊C₉	—	3	8	no	—
9	C₂×C₃²⋊C₉	C₃²	1	12	yes	—
10	C₃⁴	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₉	—	3	4	no	—
12	C₃²⋊C₉	—	3	8	no	—
13	C₃²⋊C₉	C₂×C₃²	1	12	yes	—
14	C₂×C₃³	—	3	12	no	—
15	C₂×C₃³	H(3,𝔽₃)	1	2	yes	—
16	C₂×C₃³	H(3,𝔽₃)	1	1	yes	characteristic
17	C₂×C₃³	C₃³	1	1	yes	characteristic
18	C₂×C₃×C₉	—	3	12	no	—
19	C₂×C₃×C₉	—	9	12	no	—
20	C₃³	—	3	12	no	—
21	C₃³	C₂×H(3,𝔽₃)	1	2	yes	—
22	C₃³	C₂×H(3,𝔽₃)	1	1	yes	characteristic
23	C₃³	C₂×C₃³	1	1	yes	characteristic
24	C₃×C₉	—	3	12	no	—
25	C₃×C₉	—	9	12	no	—
26	C₂×C₃²	—	3	8	no	—
27	C₂×C₃²	—	3	4	no	—
28	C₂×C₃²	—	9	9	no	—
29	C₂×C₃²	#731	1	12	yes	—
30	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₂×C₉	—	9	12	no	—
32	C₃²	—	3	8	no	—
33	C₃²	—	3	4	no	—
34	C₃²	—	9	9	no	—
35	C₃²	C₂×#731	1	12	yes	—
36	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₉	—	9	12	no	—
38	C₂×C₃	—	9	2	no	—
39	C₂×C₃	—	9	1	no	—
40	C₂×C₃	#6862	1	9	yes	direct product factor
41	C₂×C₃	C₃×#731	1	4	yes	—
42	C₃	—	9	2	no	—
43	C₃	—	9	1	no	—
44	C₃	C₂×#6862	1	9	yes	direct product factor
45	C₃	C₂×C₃×#731	1	4	yes	—
46	C₂	C₃×#6862	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃³	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₂×C₃³
prime radical	C₂×C₃⁴	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ C₂×C₃⁴ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#6862	C₂	direct (N × H)
3. C₂×#6862	C₃	direct (N × H)
5. #6862	C₂×C₃	direct (N × H)
40. C₂×C₃	#6862	direct (N × H)
44. C₃	C₂×#6862	direct (N × H)
46. C₂	C₃×#6862	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×#6862	2
C₂×C₃×C₃²⋊C₉	3
C₂×#6862	3

Subgroups — C2×C3×#6862 #13090072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#6862 #13090072