Subgroups — #34063209

Order 19197.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264253	C₃	1	3	yes	maximal
2	C₉²×C₇₉	C₃	1	1	yes	maximal, characteristic
3	#14523840	—	3	3	no	—
4	C₃×C₉×C₇₉	—	3	1	no	—
5	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
6	C₃²×C₇₉	H(3,𝔽₃)	1	1	yes	characteristic
7	C₉×C₇₉	—	3	3	no	—
8	C₉×C₇₉	—	3	1	no	—
9	C₇₉⋊C₉	—	9	3	no	—
10	#6880	—	79	1	no	maximal, Sylow
11	C₃×C₇₉	—	3	1	no	—
12	C₃×C₇₉	#732	1	1	yes	characteristic
13	#733	—	79	3	no	—
14	C₉²	C₇₉⋊C₃	1	1	yes	characteristic
15	C₇₉	#6880	1	1	yes	characteristic, complemented, Sylow
16	3₋¹⁺²	—	237	3	no	—
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
19	C₃²	C₃²⋊(C₇₉⋊C₃)	1	1	yes	characteristic
20	C₉	—	3	3	no	—
21	C₉	—	3	1	no	—
22	C₉	—	711	3	no	—
23	C₃	—	3	1	no	—
24	C₃	#20264251	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₇₉	#6880	semidirect

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