Subgroups — #31801249

Order 17739.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20238266	C₃	1	3	yes	maximal, complemented
2	C₃²×C₉×C₇₃	C₃	1	1	yes	maximal, characteristic
3	#14520291	—	3	3	no	—
4	C₃³×C₇₃	C₉	1	1	yes	characteristic
5	C₃×C₉×C₇₃	—	3	1	no	—
6	C₃×C₉×C₇₃	—	3	2	no	—
7	C₃×C₉×C₇₃	C₉	1	2	yes	—
8	C₃×C₉×C₇₃	C₃²	1	1	yes	characteristic
9	C₃²×C₇₃	—	3	3	no	—
10	C₃²×C₇₃	—	3	1	no	—
11	C₃²×C₇₃	C₃×C₉	1	1	yes	characteristic
12	C₉×C₇₃	—	3	2	no	—
13	C₉×C₇₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₉×C₇₃	3₋¹⁺²	1	2	yes	—
15	#6869	—	73	1	no	maximal, Sylow
16	C₃×C₇₃	—	3	3	no	—
17	C₃×C₇₃	—	3	1	no	—
18	C₃×C₇₃	C₃²⋊C₉	1	1	yes	characteristic
19	C₃²×C₉	C₇₃⋊C₃	1	1	yes	characteristic
20	C₂₇⋊C₃	—	73	3	no	—
21	C₇₃	#6869	1	1	yes	characteristic, complemented, Sylow
22	C₃³	#10620321	1	1	yes	characteristic
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	—	3	2	no	—
25	C₃×C₉	#10620321	1	2	yes	—
26	C₃×C₉	C₃×C₇₃⋊C₃	1	1	yes	characteristic
27	C₂₇	—	219	3	no	—
28	C₃²	—	3	3	no	—
29	C₃²	—	3	1	no	—
30	C₃²	C₃×#10620321	1	1	yes	characteristic
31	C₉	—	3	2	no	—
32	C₉	C₃²⋊(C₇₃⋊C₃)	1	1	yes	characteristic
33	C₉	#14520297	1	2	yes	—
34	C₃	—	3	1	no	—
35	C₃	—	3	3	no	—
36	C₃	C₃²⋊#10620321	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #20238266	C₃	semidirect
21. C₇₃	#6869	semidirect

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