Subgroups — #28356754

Order 13851.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095335	C₃	1	3	yes	maximal
2	C₂₇×#4294	C₃	1	1	yes	maximal, characteristic
3	#13095335	C₉	1	9	yes	complemented
4	C₃×#10587018	C₉	1	1	yes	characteristic
5	C₃×#10587018	C₃²	1	1	yes	characteristic
6	C₉×#4294	C₉	1	1	yes	characteristic
7	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
8	#10624499	—	19	1	no	maximal, Sylow
9	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
10	C₃×#4294	C₂₇	1	3	yes	—
11	C₁₉×C₂₇	C₂₇	1	3	yes	—
12	#10587018	C₂₇	1	3	yes	—
13	#10587018	C₃×C₉	1	3	yes	—
14	C₃×C₈₁	—	19	3	no	—
15	C₉×C₂₇	—	19	1	no	—
16	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
17	C₉×C₁₉	C₉²	1	1	yes	characteristic
18	C₉×C₁₉	C₃×C₂₇	1	1	yes	characteristic
19	C₉×C₁₉	C₃×C₂₇	1	1	yes	characteristic
20	#4294	—	3	3	no	—
21	C₃×C₂₇	—	19	1	no	—
22	C₃×C₂₇	—	19	1	no	—
23	C₃×C₂₇	#4296	1	1	yes	characteristic
24	C₉²	—	19	1	no	—
25	C₈₁	—	19	9	no	—
26	C₃×C₁₉	C₉×C₂₇	1	1	yes	characteristic
27	C₃×C₁₉	C₈₁⋊C₃	1	3	yes	—
28	C₃×C₉	—	19	3	no	—
29	C₃×C₉	C₃×#4296	1	1	yes	characteristic
30	C₂₇	—	19	3	no	—
31	C₂₇	—	19	3	no	—
32	C₂₇	#10587020	1	3	yes	—
33	C₁₉	#10624499	1	1	yes	characteristic, complemented, Sylow
34	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
35	C₉	—	57	3	no	—
36	C₉	C₉×#4296	1	1	yes	characteristic
37	C₉	C₃×#10587020	1	1	yes	characteristic
38	C₉	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
39	C₃	C₉×#10587020	1	1	yes	characteristic
40	C₃	#17987583	1	3	yes	—

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

N	H ≅ G/N	type
3. #13095335	C₉	semidirect
33. C₁₉	#10624499	semidirect

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