Subgroups — C₃×#19152733 #30685282

Order 17091.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152733	C₃	1	9	yes	maximal, direct product factor
2	C₃×C₂₁₁⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₃³×C₂₁₁	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₂₁₁	—	3	3	no	—
5	C₃²×C₂₁₁	C₃²	1	3	yes	—
6	C₃²×C₂₁₁	C₃²	1	1	yes	characteristic
7	C₂₁₁⋊C₉	C₃²	1	9	yes	complemented
8	C₃×C₂₁₁	—	3	3	no	—
9	C₃×C₂₁₁	3₋¹⁺²	1	3	yes	complemented
10	C₃×C₂₁₁	C₃³	1	1	yes	characteristic
11	C₂₁₁	C₃×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
12	C₃×3₋¹⁺²	—	211	1	no	maximal, Sylow
13	C₃³	C₂₁₁⋊C₃	1	1	yes	characteristic
14	3₋¹⁺²	—	211	9	no	—
15	C₃×C₉	—	211	3	no	—
16	C₃²	—	3	3	no	—
17	C₃²	C₃×C₂₁₁⋊C₃	1	3	yes	—
18	C₃²	C₃×C₂₁₁⋊C₃	1	1	yes	characteristic
19	C₉	—	211	9	no	—
20	C₃	—	3	3	no	—
21	C₃	#19152733	1	3	yes	direct product factor
22	C₃	C₃²×C₂₁₁⋊C₃	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.