Subgroups — C₃²⋊C₉×C₂₂₉ #32915313

Order 18549.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂₂₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₉×C₂₂₉	C₃	1	3	yes	maximal, complemented
3	C₃²×C₂₂₉	—	3	1	no	—
4	C₃²×C₂₂₉	—	3	2	no	—
5	C₃²×C₂₂₉	C₉	1	3	yes	complemented
6	C₃²×C₂₂₉	C₃²	1	1	yes	characteristic
7	C₉×C₂₂₉	—	3	3	no	—
8	C₃×C₂₂₉	—	3	3	no	—
9	C₃×C₂₂₉	C₃×C₉	1	1	yes	characteristic
10	C₃×C₂₂₉	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃×C₂₂₉	3₋¹⁺²	1	2	yes	—
12	C₂₂₉	C₃²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²⋊C₉	C₂₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³	C₃×C₂₂₉	1	1	yes	characteristic
15	C₃×C₉	C₃×C₂₂₉	1	3	yes	complemented
16	C₃²	—	3	1	no	—
17	C₃²	—	3	2	no	—
18	C₃²	C₉×C₂₂₉	1	3	yes	complemented
19	C₃²	C₃²×C₂₂₉	1	1	yes	characteristic
20	C₉	—	3	3	no	—
21	C₃	—	3	3	no	—
22	C₃	C₃×C₉×C₂₂₉	1	1	yes	characteristic
23	C₃	H(3,𝔽₃)×C₂₂₉	1	1	yes	characteristic
24	C₃	3₋¹⁺²×C₂₂₉	1	2	yes	—

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.