Subgroups — #41005082

Order 26973.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582510	C₃	1	2	yes	maximal
2	#22582464	C₃	1	1	yes	maximal, characteristic
3	C₃₇×#6880	C₃	1	1	yes	maximal, characteristic
4	#15688521	—	3	2	no	—
5	C₃×#11758601	—	3	1	no	—
6	C₃₇×#733	—	3	1	no	—
7	C₉²×C₃₇	C₃²	1	1	yes	characteristic
8	3₋¹⁺²×C₃₇	—	9	1	no	—
9	C₃×C₉×C₃₇	—	3	1	no	—
10	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
11	#11758608	—	9	2	no	—
12	#11758601	—	3	3	no	—
13	#10624541	—	37	1	no	maximal, Sylow
14	C₃²×C₃₇	#732	1	1	yes	characteristic
15	C₉×C₃₇	—	3	1	no	—
16	C₉×C₃₇	—	9	1	no	—
17	C₉×C₃₇	—	27	1	no	—
18	#66524	—	27	2	no	—
19	#6880	—	37	2	no	—
20	#6880	C₃₇⋊C₃	1	1	yes	characteristic
21	#6864	—	37	1	no	—
22	C₃×C₃₇	—	3	1	no	—
23	C₃×C₃₇	#6879	1	1	yes	characteristic
24	#733	—	3	1	no	—
25	#733	—	111	2	no	—
26	C₃×C₂₇	—	111	1	no	—
27	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
28	C₃₇	#10624541	1	1	yes	characteristic, complemented, Sylow
29	3₋¹⁺²	—	9	1	no	—
30	3₋¹⁺²	—	333	2	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
33	C₂₇	—	111	3	no	—
34	C₃²	#15688518	1	1	yes	characteristic
35	C₉	—	3	1	no	—
36	C₉	—	9	1	no	—
37	C₉	—	27	1	no	—
38	C₉	—	999	2	no	—
39	C₃	—	3	1	no	—
40	C₃	#22582506	1	1	yes	characteristic

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

N	H ≅ G/N	type
28. C₃₇	#10624541	semidirect

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