Subgroups — C₃⋊#10621729 #14523178

Order 2028.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	#10621729	—	3	1	no	maximal, Hall
3	C₃×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊D₁₃	D₃	1	1	yes	characteristic
5	C₁₃²	Dic₃	1	1	yes	characteristic, complemented, Sylow
6	C₃⋊#261	—	13	2	no	maximal
7	C₃×D₁₃	—	13	2	no	—
8	C₃×D₁₃	—	26	6	no	—
9	#261	—	39	2	no	—
10	C₃×C₁₃	—	2	6	no	—
11	C₃×C₁₃	#261	1	2	yes	complemented
12	D₁₃	—	13	2	no	—
13	D₁₃	—	26	6	no	—
14	C₁₃	—	2	6	no	—
15	C₁₃	C₃⋊#261	1	2	yes	complemented
16	Dic₃	—	169	1	no	Hall
17	C₂×C₃	—	169	1	no	—
18	C₄	—	507	1	no	Sylow
19	C₃	#10621729	1	1	yes	characteristic, complemented, Sylow
20	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃²	C₄
prime radical, cosocle	C₃×C₁₃⋊D₁₃	C₂
LCS	G ▷ C₃×C₁₃²
UCS	C₁

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.