Subgroups — C₃₇×#92789 #34037293

Order 18759.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×C₁₃⋊C₃	—	13	2	no	maximal
3	#92789	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₃₇	—	3	4	no	—
5	C₁₃×C₃₇	C₁₃⋊C₃	1	2	yes	complemented
6	C₁₃²	C₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₃₇	—	169	1	no	Hall
8	C₁₃⋊C₃	—	13	2	no	—
9	C₃₇	#92789	1	1	yes	characteristic, direct product factor, Sylow
10	C₁₃	—	3	4	no	—
11	C₁₃	C₃₇×C₁₃⋊C₃	1	2	yes	complemented
12	C₃	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	#92789
commutator, cosocle, hypocenter	C₁₃²	C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₁₃²×C₃₇	C₃
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₃₇

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.