Subgroups — #21419273

Order 7533.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578900	C₃	1	2	yes	maximal, complemented
2	#14578886	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#733	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×C₃₁	—	3	1	no	—
5	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
6	C₃²⋊(C₃₁⋊C₃)	—	3	2	no	—
7	C₃×C₃₁⋊C₉	—	3	1	no	—
8	C₃²×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₃₁⋊C₃	—	9	2	no	—
10	C₉×C₃₁	—	3	1	no	—
11	C₉×C₃₁	—	9	1	no	—
12	C₃₁⋊C₉	—	9	1	no	—
13	#6881	—	31	1	no	maximal, Sylow
14	C₃×C₃₁	—	3	1	no	—
15	C₃×C₃₁	#732	1	1	yes	characteristic
16	C₃₁⋊C₃	—	27	2	no	—
17	#733	C₃₁⋊C₃	1	1	yes	characteristic, complemented
18	#732	—	31	2	no	—
19	C₉⋊C₉	—	31	1	no	—
20	C₃₁	#6881	1	1	yes	characteristic, complemented, Sylow
21	3₋¹⁺²	—	3	1	no	—
22	H(3,𝔽₃)	—	93	2	no	—
23	C₃×C₉	—	93	1	no	—
24	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
25	C₃²	—	279	2	no	—
26	C₃²	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	9	1	no	—
29	C₉	—	279	1	no	—
30	C₃	—	3	1	no	—
31	C₃	—	837	2	no	—
32	C₃	#14578899	1	1	yes	characteristic

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