Subgroups — #21419265

Order 7533.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578900	C₃	1	3	yes	maximal, complemented
2	C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×C₃₁	—	3	1	no	—
4	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
5	C₃²⋊(C₃₁⋊C₃)	—	3	3	no	—
6	C₃²×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
7	C₃×C₃₁⋊C₃	—	9	3	no	—
8	C₉×C₃₁	—	3	3	no	—
9	C₉×C₃₁	—	3	1	no	—
10	#6879	—	31	1	no	maximal, Sylow
11	C₃×C₃₁	—	3	1	no	—
12	C₃×C₃₁	#732	1	1	yes	characteristic
13	C₃₁⋊C₃	—	27	3	no	—
14	#732	—	31	3	no	—
15	C₉²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
16	C₃₁	#6879	1	1	yes	characteristic, complemented, Sylow
17	H(3,𝔽₃)	—	93	3	no	—
18	C₃×C₉	—	3	1	no	—
19	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
20	C₃²	—	279	3	no	—
21	C₃²	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
22	C₉	—	3	3	no	—
23	C₉	—	3	1	no	—
24	C₃	—	3	1	no	—
25	C₃	—	837	3	no	—
26	C₃	#14578900	1	1	yes	characteristic

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