Subgroups — #28356837

Order 13851.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987549	C₃	1	3	yes	maximal, complemented
2	C₃×#13095301	C₃	1	1	yes	maximal, characteristic
3	#13095301	C₉	1	2	yes	—
4	#13095301	C₃²	1	1	yes	characteristic
5	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
6	C₂₄₃⋊C₃	—	19	1	no	maximal, Sylow
7	C₃×C₉×C₁₉	C₂₇	1	1	yes	characteristic
8	C₁₉×C₂₇	C₂₇	1	2	yes	—
9	C₁₉×C₂₇	C₃×C₉	1	1	yes	characteristic
10	C₃×C₈₁	—	19	1	no	—
11	C₂₄₃	—	19	3	no	—
12	C₃²×C₁₉	C₈₁	1	1	yes	characteristic
13	C₉×C₁₉	C₈₁	1	2	yes	—
14	C₉×C₁₉	C₃×C₂₇	1	1	yes	characteristic
15	C₃×C₂₇	#4296	1	1	yes	characteristic
16	C₈₁	—	19	2	no	—
17	C₈₁	—	19	1	no	—
18	C₃×C₁₉	—	3	1	no	—
19	C₃×C₁₉	C₃×C₈₁	1	1	yes	characteristic
20	C₃×C₉	#10587020	1	1	yes	characteristic
21	C₂₇	#10587020	1	2	yes	—
22	C₂₇	C₃×#4296	1	1	yes	characteristic
23	C₁₉	C₂₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃²	#13095335	1	1	yes	characteristic
25	C₉	#13095335	1	2	yes	—
26	C₉	C₃×#10587020	1	1	yes	characteristic
27	C₃	—	3	1	no	—
28	C₃	C₃×#13095335	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #17987549	C₃	semidirect
23. C₁₉	C₂₄₃⋊C₃	semidirect

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