Subgroups — #38736502

Order 25029.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22552470	C₃	1	2	yes	maximal, complemented
2	#22552468	C₃	1	1	yes	maximal, characteristic
3	C₉⋊C₉×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
4	#14584009	—	3	2	no	—
5	C₃²⋊(C₁₀₃⋊C₃)	—	3	1	no	—
6	C₃×C₉×C₁₀₃	—	3	1	no	—
7	C₃×C₉×C₁₀₃	C₃²	1	1	yes	characteristic
8	C₃²×C₁₀₃	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₁₀₃⋊C₃	—	9	1	no	—
10	C₉×C₁₀₃	—	3	1	no	—
11	C₉×C₁₀₃	—	9	1	no	—
12	C₁₀₃⋊C₉	—	9	2	no	—
13	C₃×C₁₀₃	—	3	1	no	—
14	C₃×C₁₀₃	#732	1	1	yes	characteristic
15	C₁₀₃⋊C₃	—	27	1	no	—
16	#6883	—	103	1	no	maximal, Sylow
17	C₁₀₃	#6883	1	1	yes	characteristic, complemented, Sylow
18	#733	—	103	2	no	—
19	#732	—	103	1	no	—
20	C₉⋊C₉	C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
21	3₋¹⁺²	—	309	2	no	—
22	H(3,𝔽₃)	—	309	1	no	—
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic
25	C₃²	—	927	1	no	—
26	C₃²	C₃²⋊(C₁₀₃⋊C₃)	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	9	1	no	—
29	C₉	—	927	2	no	—
30	C₃	—	3	1	no	—
31	C₃	—	2781	1	no	—
32	C₃	#22552468	1	1	yes	characteristic

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.