Subgroups — C₃₇×#11725131 #45658455

Order 32708.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×D₂₂₁	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₇×#595	—	13	1	no	maximal, Hall
4	C₃₇×#261	—	17	1	no	maximal, Hall
5	D₁₇×C₃₇	—	13	1	no	—
6	D₁₃×C₃₇	—	17	1	no	—
7	#11725131	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₃₇	#261	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₇	#595	1	1	yes	characteristic, complemented, Hall
10	D₂₂₁	C₂×C₃₇	1	1	yes	characteristic
11	C₁₃×C₁₇	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
12	C₄×C₃₇	—	221	1	no	Hall
13	C₂×C₃₇	—	221	1	no	—
14	#595	—	13	1	no	Hall
15	#261	—	17	1	no	Hall
16	C₃₇	#11725131	1	1	yes	characteristic, direct product factor, Sylow
17	D₁₇	—	13	1	no	—
18	D₁₃	—	17	1	no	—
19	C₁₇	C₃₇×#261	1	1	yes	characteristic, complemented, Sylow
20	C₁₃	C₃₇×#595	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	221	1	no	Sylow
22	C₂	—	221	1	no	—

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.