Subgroups — C₂×(C₃³⋊C₁₃)⋊C₃ #72224468

Order 2106.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃³⋊C₁₃)⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃³⋊C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃³⋊C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
4	C₂×AΣL(1,𝔽₂₇)	—	13	1	no	maximal, Hall
5	AΣL(1,𝔽₂₇)	—	13	1	no	Sylow
6	C₂×C₁₃⋊C₃	—	27	1	no	maximal
7	C₂×C₃³	C₁₃⋊C₃	1	1	yes	characteristic, complemented
8	C₂×3₋¹⁺²	—	13	2	no	—
9	C₂×H(3,𝔽₃)	—	13	1	no	—
10	C₁₃⋊C₃	—	27	1	no	—
11	C₃³	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
12	3₋¹⁺²	—	13	2	no	—
13	H(3,𝔽₃)	—	13	1	no	—
14	C₂×C₁₃	—	27	1	no	Hall
15	C₂×C₃²	—	13	1	no	—
16	C₂×C₃²	—	39	1	no	—
17	C₂×C₉	—	39	2	no	—
18	C₁₃	—	27	1	no	Sylow
19	C₃²	—	13	1	no	—
20	C₃²	—	39	1	no	—
21	C₉	—	39	2	no	—
22	C₂×C₃	—	13	1	no	—
23	C₂×C₃	—	117	1	no	—
24	C₃	—	13	1	no	—
25	C₃	—	117	1	no	—
26	C₂	(C₃³⋊C₁₃)⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	(C₃³⋊C₁₃)⋊C₃
commutator, cosocle, hypocenter	C₃³⋊C₁₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃³	C₁₃⋊C₃
LCS	G ▷ C₃³⋊C₁₃
UCS	C₁ ◁ C₂

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

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