Subgroups — #28356753

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	C₉×#10587018	C₃	1	1	yes	maximal, characteristic
3	#13095335	C₉	1	9	yes	complemented
4	C₃×#10587018	C₉	1	2	yes	—
5	C₃×#10587018	C₃²	1	1	yes	characteristic
6	C₉²×C₁₉	C₉	1	1	yes	characteristic
7	#10624499	—	19	1	no	maximal, Sylow
8	C₃×C₉×C₁₉	C₂₇	1	3	yes	—
9	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
10	#10587018	C₂₇	1	6	yes	—
11	#10587018	C₃×C₉	1	3	yes	—
12	C₃×C₈₁	—	19	3	no	—
13	C₉×C₂₇	—	19	1	no	—
14	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
15	C₉×C₁₉	—	3	3	no	—
16	C₉×C₁₉	C₉²	1	1	yes	characteristic
17	C₉×C₁₉	C₃×C₂₇	1	2	yes	—
18	C₃×C₂₇	—	19	2	no	—
19	C₃×C₂₇	—	19	1	no	—
20	C₉²	#4296	1	1	yes	characteristic
21	C₈₁	—	19	9	no	—
22	C₃×C₁₉	C₉×C₂₇	1	1	yes	characteristic
23	C₃×C₁₉	C₈₁⋊C₃	1	3	yes	—
24	C₃×C₉	#10587020	1	3	yes	—
25	C₃×C₉	C₃×#4296	1	1	yes	characteristic
26	C₂₇	—	19	3	no	—
27	C₂₇	—	19	6	no	—
28	C₁₉	#10624499	1	1	yes	characteristic, complemented, Sylow
29	C₃²	C₃×#10587020	1	1	yes	characteristic
30	C₉	—	3	3	no	—
31	C₉	C₉×#4296	1	1	yes	characteristic
32	C₉	(C₁₉⋊C₃)⋊C₂₇	1	2	yes	—
33	C₃	C₉×#10587020	1	1	yes	characteristic
34	C₃	#17987582	1	3	yes	—

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

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

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