Subgroups — #41004737

Order 26973.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11758601	C₃	1	3	yes	maximal
2	C₉×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×#11758601	C₉	1	9	yes	—
4	C₃×C₂₇×C₃₇	C₉	1	3	yes	—
5	C₉²×C₃₇	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
7	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
8	C₂₇×C₃₇	C₂₇	1	9	yes	complemented
9	#11758601	—	3	9	no	—
10	#10624443	—	37	1	no	maximal, Sylow
11	C₃²×C₃₇	C₉²	1	1	yes	characteristic
12	C₉×C₃₇	C₃×C₂₇	1	3	yes	—
13	C₉×C₃₇	C₂₇⋊C₃	1	9	yes	—
14	C₉×C₂₇	—	37	3	no	—
15	C₉×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
16	C₃×C₃₇	C₉×C₂₇	1	1	yes	characteristic
17	C₃×C₃₇	#6864	1	3	yes	—
18	C₃×C₂₇	—	37	9	no	—
19	C₃×C₂₇	#66524	1	3	yes	—
20	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
21	C₃₇	#10624443	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₉	C₉×C₃₇⋊C₃	1	3	yes	—
23	C₃×C₉	C₃×#66524	1	1	yes	characteristic
24	C₂₇	—	111	9	no	—
25	C₂₇	#11758601	1	9	yes	complemented
26	C₃²	C₉×#66524	1	1	yes	characteristic
27	C₉	C₃×#11758601	1	3	yes	—
28	C₉	#15688510	1	9	yes	—
29	C₃	C₉×#11758601	1	1	yes	characteristic
30	C₃	#22582463	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.