Subgroups — #41008348

Order 26973.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688534	C₃	1	3	yes	maximal
2	C₂₇×#66524	C₃	1	1	yes	maximal, characteristic
3	#15688534	C₉	1	9	yes	complemented
4	C₃×#11758601	C₉	1	1	yes	characteristic
5	C₃×#11758601	C₃²	1	1	yes	characteristic
6	C₉×#66524	C₉	1	1	yes	characteristic
7	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
8	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₃×#66524	C₂₇	1	3	yes	—
10	C₂₇×C₃₇	C₂₇	1	3	yes	—
11	#11758601	C₂₇	1	3	yes	—
12	#11758601	C₃×C₉	1	3	yes	—
13	#10624499	—	37	1	no	maximal, Sylow
14	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
15	C₉×C₃₇	C₉²	1	1	yes	characteristic
16	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
17	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
18	#66524	—	3	3	no	—
19	C₃×C₈₁	—	37	3	no	—
20	C₉×C₂₇	—	37	1	no	—
21	C₃×C₃₇	C₉×C₂₇	1	1	yes	characteristic
22	C₃×C₃₇	C₈₁⋊C₃	1	3	yes	—
23	C₃×C₂₇	—	37	1	no	—
24	C₃×C₂₇	—	37	1	no	—
25	C₃×C₂₇	#66526	1	1	yes	characteristic
26	C₉²	—	37	1	no	—
27	C₈₁	—	37	9	no	—
28	C₃₇	#10624499	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₉	—	37	3	no	—
30	C₃×C₉	C₃×#66526	1	1	yes	characteristic
31	C₂₇	—	37	3	no	—
32	C₂₇	—	37	3	no	—
33	C₂₇	#11758603	1	3	yes	—
34	C₃²	(C₃₇⋊C₃)⋊C₂₇	1	1	yes	characteristic
35	C₉	—	111	3	no	—
36	C₉	C₉×#66526	1	1	yes	characteristic
37	C₉	C₃×#11758603	1	1	yes	characteristic
38	C₉	(C₃₇⋊C₃)⋊C₂₇	1	1	yes	characteristic
39	C₃	C₉×#11758603	1	1	yes	characteristic
40	C₃	#22582717	1	3	yes	—

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

N	H ≅ G/N	type
3. #15688534	C₉	semidirect
28. C₃₇	#10624499	semidirect

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