Subgroups — C₃⋊#14523824 #20264196

Order 6396.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₄₁	C₂	1	1	yes	maximal, characteristic
2	#14523824	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₄₁	D₃	1	1	yes	characteristic
5	C₁₃×C₄₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#4223	—	13	1	no	maximal, Hall
7	C₃×D₄₁	D₁₃	1	1	yes	characteristic
8	#4223	—	39	1	no	Hall
9	Dic₃₉	—	41	1	no	maximal, Hall
10	C₃×C₄₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
11	D₄₁	D₃₉	1	1	yes	characteristic
12	C₂×C₃×C₁₃	—	41	1	no	—
13	Dic₁₃	—	123	1	no	Hall
14	C₄₁	Dic₃₉	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₃	#4223	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	—	41	1	no	—
17	C₁₃	C₃⋊#4223	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	533	1	no	Hall
19	C₂×C₃	—	41	1	no	—
20	C₄	—	1599	1	no	Sylow
21	C₃	#14523824	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	41	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃×C₄₁	C₄
LCS	G ▷ C₃×C₁₃×C₄₁
UCS	C₁

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