Subgroups — #46798513

Order 33777.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014619	C₃	1	2	yes	maximal
2	C₉×C₁₃₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	#733×C₁₃₉	C₃	1	1	yes	maximal, characteristic
4	#16836730	—	3	2	no	—
5	C₃×C₁₃₉⋊C₉	—	3	1	no	—
6	3₋¹⁺²×C₁₃₉	—	3	1	no	—
7	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
8	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
9	C₉×C₁₃₉	—	3	1	no	—
10	C₉×C₁₃₉	—	9	1	no	—
11	C₁₃₉⋊C₉	—	3	3	no	—
12	C₁₃₉⋊C₉	—	9	2	no	—
13	C₃×C₁₃₉	—	3	1	no	—
14	C₃×C₁₃₉	#732	1	1	yes	characteristic
15	#6880	—	139	1	no	maximal, Sylow
16	C₁₃₉	#6880	1	1	yes	characteristic, complemented, Sylow
17	#733	—	139	2	no	—
18	#733	C₁₃₉⋊C₃	1	1	yes	characteristic
19	C₉²	—	139	1	no	—
20	3₋¹⁺²	—	3	1	no	—
21	3₋¹⁺²	—	417	2	no	—
22	C₃×C₉	—	417	1	no	—
23	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
24	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
25	C₉	—	3	1	no	—
26	C₉	—	9	1	no	—
27	C₉	—	417	3	no	—
28	C₉	—	1251	2	no	—
29	C₃	—	3	1	no	—
30	C₃	#26014616	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₁₃₉	#6880	semidirect

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