Subgroups — C₂×#6882 #92244

Order 486.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6882	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#733	C₃	1	3	yes	maximal
3	C₂×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	#733	C₂×C₃	1	3	yes	—
5	C₉⋊C₉	C₂×C₃	1	1	yes	characteristic
6	C₂×3₋¹⁺²	—	3	3	no	—
7	C₂×C₃×C₉	—	3	1	no	—
8	C₂×C₃×C₉	C₃²	1	1	yes	characteristic
9	3₋¹⁺²	—	3	3	no	—
10	C₃×C₉	—	3	1	no	—
11	C₃×C₉	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
13	C₂×C₉	—	3	1	no	—
14	C₂×C₉	—	9	1	no	—
15	C₂×C₉	—	9	3	no	—
16	C₃²	C₂×H(3,𝔽₃)	1	1	yes	characteristic
17	C₉	—	3	1	no	—
18	C₉	—	9	1	no	—
19	C₉	—	9	3	no	—
20	C₂×C₃	—	3	1	no	—
21	C₂×C₃	#732	1	1	yes	characteristic
22	C₃	—	3	1	no	—
23	C₃	C₂×#732	1	1	yes	characteristic
24	C₂	#6882	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃	#732
commutator, Frattini, cosocle	C₃×C₉	C₂×C₃²
prime radical	C₂×C₃²	H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃² ◁ C₂×C₃×C₉ ◁ G

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

N	H ≅ G/N	type
1. #6882	C₂	direct (N × H)
24. C₂	#6882	direct (N × H)

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