Subgroups — #37555839

Order 23571.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21463367	C₃	1	3	yes	maximal
2	C₉⋊C₉×C₉₇	C₃	1	1	yes	maximal, characteristic
3	#14579757	—	3	3	no	—
4	C₃×C₉×C₉₇	—	3	1	no	—
5	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
6	C₃²×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
7	C₉×C₉₇	—	3	1	no	—
8	C₉×C₉₇	—	9	1	no	—
9	C₉₇⋊C₉	—	9	3	no	—
10	C₃×C₉₇	—	3	1	no	—
11	C₃×C₉₇	#732	1	1	yes	characteristic
12	#6882	—	97	1	no	maximal, Sylow
13	C₉₇	#6882	1	1	yes	characteristic, complemented, Sylow
14	#733	—	97	3	no	—
15	C₉⋊C₉	C₉₇⋊C₃	1	1	yes	characteristic
16	3₋¹⁺²	—	291	3	no	—
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic
19	C₃²	C₃²⋊(C₉₇⋊C₃)	1	1	yes	characteristic
20	C₉	—	3	1	no	—
21	C₉	—	9	1	no	—
22	C₉	—	873	3	no	—
23	C₃	—	3	1	no	—
24	C₃	#21463365	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₉₇	#6882	semidirect

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