Subgroups — #31801247

Order 17739.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#10620321	C₃	1	3	yes	maximal
2	C₃²×C₉×C₇₃	C₃	1	1	yes	maximal, characteristic
3	C₃×#10620321	—	3	3	no	—
4	C₃³×C₇₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₇₃	—	3	1	no	—
6	C₃×C₉×C₇₃	—	3	2	no	—
7	C₃×C₉×C₇₃	C₉	1	3	yes	complemented
8	C₃²×C₇₃	—	3	1	no	—
9	C₃²×C₇₃	—	3	2	no	—
10	C₃²×C₇₃	C₃×C₉	1	1	yes	characteristic
11	C₃²×C₇₃	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃²×C₇₃	3₋¹⁺²	1	2	yes	—
13	C₉×C₇₃	—	3	3	no	—
14	#10620321	—	9	3	no	—
15	#6868	—	73	1	no	maximal, Sylow
16	C₃×C₇₃	—	3	1	no	—
17	C₃×C₇₃	—	3	2	no	—
18	C₃×C₇₃	C₃²⋊C₉	1	1	yes	characteristic
19	C₃×C₇₃	#732	1	1	yes	characteristic
20	C₃×C₇₃	#733	1	2	yes	—
21	C₃²×C₉	C₇₃⋊C₃	1	1	yes	characteristic
22	C₃²⋊C₉	—	73	3	no	—
23	C₇₃	#6868	1	1	yes	characteristic, complemented, Sylow
24	C₃³	C₃×C₇₃⋊C₃	1	1	yes	characteristic
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	—	3	2	no	—
27	C₃×C₉	—	219	3	no	—
28	C₃×C₉	#10620321	1	3	yes	complemented
29	C₃²	—	3	1	no	—
30	C₃²	—	3	2	no	—
31	C₃²	C₃×#10620321	1	1	yes	characteristic
32	C₃²	C₃²⋊(C₇₃⋊C₃)	1	1	yes	characteristic
33	C₃²	#14520297	1	2	yes	—
34	C₉	—	3	3	no	—
35	C₉	—	657	3	no	—
36	C₃	—	3	1	no	—
37	C₃	—	3	2	no	—
38	C₃	C₃²⋊#10620321	1	1	yes	characteristic
39	C₃	#20238274	1	1	yes	characteristic
40	C₃	#20238276	1	2	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.