Subgroups — C₃×#14523840 #20264261

Order 6399.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14523840	C₃	1	9	yes	maximal, direct product factor
2	C₃×C₇₉⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₃³×C₇₉	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₇₉	—	3	3	no	—
5	C₃²×C₇₉	C₃²	1	3	yes	—
6	C₃²×C₇₉	C₃²	1	1	yes	characteristic
7	C₇₉⋊C₉	C₃²	1	9	yes	complemented
8	C₃×C₇₉	—	3	3	no	—
9	C₃×C₇₉	3₋¹⁺²	1	3	yes	complemented
10	C₃×C₇₉	C₃³	1	1	yes	characteristic
11	C₃×3₋¹⁺²	—	79	1	no	maximal, Sylow
12	C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
13	C₃³	C₇₉⋊C₃	1	1	yes	characteristic
14	3₋¹⁺²	—	79	9	no	—
15	C₃×C₉	—	79	3	no	—
16	C₃²	—	3	3	no	—
17	C₃²	C₃×C₇₉⋊C₃	1	3	yes	—
18	C₃²	C₃×C₇₉⋊C₃	1	1	yes	characteristic
19	C₉	—	79	9	no	—
20	C₃	—	3	3	no	—
21	C₃	#14523840	1	3	yes	direct product factor
22	C₃	C₃²×C₇₉⋊C₃	1	1	yes	characteristic

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