Subgroups — #13133510

Order 1701.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	#10588039	C₃	1	3	yes	maximal
3	#6882	—	7	1	no	maximal, Sylow
4	C₃×C₇×C₉	—	3	1	no	—
5	C₃×C₇×C₉	C₃²	1	1	yes	characteristic
6	#4430	—	3	3	no	—
7	#733	—	7	3	no	—
8	C₉⋊C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
9	C₃²×C₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₇×C₉	—	3	1	no	—
11	C₇×C₉	—	9	1	no	—
12	C₇⋊C₉	—	9	3	no	—
13	3₋¹⁺²	—	21	3	no	—
14	C₃×C₉	—	3	1	no	—
15	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₃×C₇	—	3	1	no	—
17	C₃×C₇	#732	1	1	yes	characteristic
18	C₃²	C₇⋊H(3,𝔽₃)	1	1	yes	characteristic
19	C₉	—	3	1	no	—
20	C₉	—	9	1	no	—
21	C₉	—	63	3	no	—
22	C₇	#6882	1	1	yes	characteristic, complemented, Sylow
23	C₃	—	3	1	no	—
24	C₃	#10588038	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₇	#6882	semidirect

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