Subgroups — #28356832

Order 13851.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987582	C₃	1	3	yes	maximal
2	#17987331	C₃	1	1	yes	maximal, characteristic
3	#13095335	—	3	3	no	—
4	C₃×#10587018	C₉	1	1	yes	characteristic
5	C₃×#10587018	C₉	1	1	yes	characteristic
6	C₃×#10587018	C₃²	1	1	yes	characteristic
7	C₉²×C₁₉	C₉	1	1	yes	characteristic
8	#10624532	—	19	1	no	maximal, Sylow
9	C₃×C₉×C₁₉	—	3	1	no	—
10	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
11	#10587018	—	3	1	no	—
12	#10587018	C₂₇	1	3	yes	—
13	#10587018	3₋¹⁺²	1	3	yes	—
14	C₈₁⋊C₃	—	19	3	no	—
15	#6864	—	19	1	no	—
16	C₃²×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
17	C₉×C₁₉	—	9	1	no	—
18	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
19	C₉×C₁₉	C₃×C₂₇	1	1	yes	characteristic
20	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
21	C₃×C₂₇	—	19	1	no	—
22	C₃×C₂₇	—	19	1	no	—
23	C₃×C₂₇	—	19	1	no	—
24	C₉²	#4296	1	1	yes	characteristic
25	C₈₁	—	57	3	no	—
26	C₃×C₁₉	—	3	1	no	—
27	C₃×C₁₉	C₉⋊C₂₇	1	1	yes	characteristic
28	C₃×C₉	—	3	1	no	—
29	C₃×C₉	C₃×#4296	1	1	yes	characteristic
30	C₂₇	—	19	3	no	—
31	C₂₇	—	19	3	no	—
32	C₂₇	—	57	1	no	—
33	C₁₉	#10624532	1	1	yes	characteristic, complemented, Sylow
34	C₃²	#13095342	1	1	yes	characteristic
35	C₉	—	9	1	no	—
36	C₉	#13095339	1	1	yes	characteristic
37	C₉	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
38	C₉	#13095343	1	1	yes	characteristic
39	C₃	—	3	1	no	—
40	C₃	#17987573	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₁₉	#10624532	semidirect

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