Subgroups — #41005066

Order 26973.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582510	C₃	1	2	yes	maximal, complemented
2	#22582507	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
4	#15688521	—	3	2	no	—
5	#15688519	—	3	1	no	—
6	C₃×C₂₇×C₃₇	—	3	1	no	—
7	C₉²×C₃₇	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₃₇	—	3	1	no	—
9	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃²⋊(C₃₇⋊C₃)	—	9	1	no	—
11	#11758608	—	9	2	no	—
12	C₂₇×C₃₇	—	3	3	no	—
13	#10624537	—	37	1	no	maximal, Sylow
14	C₃²×C₃₇	#732	1	1	yes	characteristic
15	C₃×C₃₇⋊C₃	—	27	1	no	—
16	C₉×C₃₇	—	3	3	no	—
17	C₉×C₃₇	—	3	1	no	—
18	#66524	—	27	2	no	—
19	#6880	—	37	2	no	—
20	#6879	—	37	1	no	—
21	C₉×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic, complemented
22	C₃×C₃₇	—	3	1	no	—
23	C₃×C₃₇	#6879	1	1	yes	characteristic
24	C₃₇⋊C₃	—	81	1	no	—
25	#733	—	111	2	no	—
26	#732	—	111	1	no	—
27	C₃×C₂₇	—	3	1	no	—
28	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
29	C₃₇	#10624537	1	1	yes	characteristic, complemented, Sylow
30	3₋¹⁺²	—	333	2	no	—
31	H(3,𝔽₃)	—	333	1	no	—
32	C₃×C₉	—	3	1	no	—
33	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
34	C₂₇	—	3	3	no	—
35	C₃²	—	999	1	no	—
36	C₃²	#15688519	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	3	1	no	—
39	C₉	—	999	2	no	—
40	C₃	—	3	1	no	—
41	C₃	—	2997	1	no	—
42	C₃	#22582507	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.