Subgroups — #41007317

Order 26973.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582500	C₃	1	8	yes	maximal, complemented
2	C₃×#15688500	C₃	1	4	yes	maximal, complemented
3	C₃₇×#6903	C₃	1	1	yes	maximal, characteristic
4	#15688500	C₃²	1	1	yes	characteristic
5	#15688500	C₃²	1	8	yes	—
6	C₃₇×#737	C₉	1	1	yes	characteristic
7	C₃₇×C₂₇⋊C₃	C₉	1	8	yes	—
8	C₃×C₂₇×C₃₇	C₃²	1	4	yes	—
9	3₋¹⁺²×C₃₇	C₂₇	1	8	yes	—
10	H(3,𝔽₃)×C₃₇	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₃×C₉	1	4	yes	—
12	C₂₇×C₃₇	C₃×C₉	1	8	yes	—
13	C₂₇×C₃₇	C₃³	1	1	yes	characteristic
14	#10624833	—	37	1	no	maximal, Sylow
15	C₃²×C₃₇	C₃×C₂₇	1	4	yes	—
16	C₉×C₃₇	C₃×C₂₇	1	8	yes	—
17	C₉×C₃₇	C₃²×C₉	1	1	yes	characteristic
18	#6903	C₃₇⋊C₃	1	1	yes	characteristic
19	C₈₁⋊C₃	—	37	8	no	—
20	C₃×C₈₁	—	37	4	no	—
21	C₃×C₃₇	—	3	4	no	—
22	C₃×C₃₇	C₃²×C₂₇	1	1	yes	characteristic
23	#737	#66524	1	1	yes	characteristic
24	C₂₇⋊C₃	#66524	1	8	yes	—
25	C₃×C₂₇	C₃×C₃₇⋊C₃	1	4	yes	—
26	C₈₁	—	37	1	no	—
27	C₈₁	—	37	8	no	—
28	C₃₇	#10624833	1	1	yes	characteristic, complemented, Sylow
29	3₋¹⁺²	#11758601	1	8	yes	—
30	H(3,𝔽₃)	#11758601	1	1	yes	characteristic
31	C₃×C₉	C₃×#66524	1	4	yes	—
32	C₂₇	C₃×#66524	1	8	yes	—
33	C₂₇	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
34	C₃²	C₃×#11758601	1	4	yes	—
35	C₉	C₃×#11758601	1	8	yes	—
36	C₉	C₃²×#66524	1	1	yes	characteristic
37	C₃	—	3	4	no	—
38	C₃	C₃²×#11758601	1	1	yes	characteristic

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.