Subgroups — C₂×#6858 #92220

Order 486.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6858	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃²⋊C₉	C₃	1	2	yes	maximal
5	C₃×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
6	C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
7	C₃²⋊C₉	C₂×C₃	1	2	yes	—
8	C₂×C₃³	C₃²	1	1	yes	characteristic
9	C₂×3₋¹⁺²	—	3	3	no	—
10	C₂×C₃×C₉	—	3	1	no	—
11	C₂×C₃×C₉	—	3	1	no	—
12	C₂×C₃×C₉	—	3	2	no	—
13	C₃³	C₂×C₃²	1	1	yes	characteristic
14	3₋¹⁺²	—	3	3	no	—
15	C₃×C₉	—	3	1	no	—
16	C₃×C₉	—	3	1	no	—
17	C₃×C₉	—	3	2	no	—
18	C₂×C₃²	—	3	1	no	—
19	C₂×C₃²	—	3	2	no	—
20	C₂×C₃²	—	3	1	no	—
21	C₂×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
22	C₂×C₉	—	3	3	no	—
23	C₂×C₉	—	9	1	no	—
24	C₂×C₉	—	9	2	no	—
25	C₃²	—	3	1	no	—
26	C₃²	—	3	2	no	—
27	C₃²	—	3	1	no	—
28	C₃²	C₂×H(3,𝔽₃)	1	1	yes	characteristic
29	C₉	—	3	3	no	—
30	C₉	—	9	1	no	—
31	C₉	—	9	2	no	—
32	C₂×C₃	—	9	1	no	—
33	C₂×C₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
34	C₂×C₃	#731	1	2	yes	—
35	C₂×C₃	#733	1	1	yes	characteristic
36	C₃	—	9	1	no	—
37	C₃	C₂×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
38	C₃	C₂×#731	1	2	yes	—
39	C₃	C₂×#733	1	1	yes	characteristic
40	C₂	#6858	1	1	yes	characteristic, direct product factor, Sylow

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

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

N	H ≅ G/N	type
1. #6858	C₂	direct (N × H)
40. C₂	#6858	direct (N × H)

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