Subgroups — #28356673

Order 13851.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#10587020	C₃	1	3	yes	maximal
2	C₂₇×#4294	C₃	1	1	yes	maximal, characteristic
3	C₃×#10587020	C₉	1	9	yes	—
4	C₃×#10587018	C₉	1	2	yes	—
5	C₉×#4294	C₃²	1	1	yes	characteristic
6	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
7	#10624443	—	19	1	no	maximal, Sylow
8	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
9	C₃×#4294	C₃×C₉	1	3	yes	—
10	#10587020	—	3	9	no	—
11	C₁₉×C₂₇	C₂₇	1	3	yes	complemented
12	#10587018	C₂₇	1	6	yes	complemented
13	C₉×C₂₇	—	19	3	no	—
14	C₉×C₂₇	—	19	1	no	—
15	C₃²×C₁₉	C₉²	1	1	yes	characteristic
16	C₉×C₁₉	C₃×C₂₇	1	1	yes	characteristic
17	C₉×C₁₉	C₃×C₂₇	1	2	yes	—
18	#4294	C₂₇⋊C₃	1	9	yes	—
19	C₃×C₂₇	—	19	2	no	—
20	C₃×C₂₇	—	19	9	no	—
21	C₃×C₂₇	#4296	1	1	yes	characteristic
22	C₉²	—	19	1	no	—
23	C₃×C₁₉	C₉×C₂₇	1	1	yes	characteristic
24	C₃×C₁₉	#6864	1	3	yes	—
25	C₃×C₉	—	19	3	no	—
26	C₃×C₉	C₃×#4296	1	1	yes	characteristic
27	C₂₇	—	19	6	no	—
28	C₂₇	—	57	9	no	—
29	C₂₇	#10587020	1	3	yes	complemented
30	C₁₉	#10624443	1	1	yes	characteristic, complemented, Sylow
31	C₃²	C₉×#4296	1	1	yes	characteristic
32	C₉	—	19	9	no	—
33	C₉	C₃×#10587020	1	1	yes	characteristic
34	C₉	(C₁₉⋊C₃)⋊C₂₇	1	2	yes	—
35	C₃	C₉×#10587020	1	1	yes	characteristic
36	C₃	#17987554	1	3	yes	—

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

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