Subgroups — C₃²⋊C₉×C₂₄₁ #34085992

Order 19521.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂₄₁	C₃	1	1	yes	maximal, characteristic
2	C₃×C₉×C₂₄₁	C₃	1	3	yes	maximal, complemented
3	C₃²×C₂₄₁	—	3	1	no	—
4	C₃²×C₂₄₁	—	3	2	no	—
5	C₃²×C₂₄₁	C₉	1	3	yes	complemented
6	C₃²×C₂₄₁	C₃²	1	1	yes	characteristic
7	C₉×C₂₄₁	—	3	3	no	—
8	C₃×C₂₄₁	—	3	3	no	—
9	C₃×C₂₄₁	C₃×C₉	1	1	yes	characteristic
10	C₃×C₂₄₁	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃×C₂₄₁	3₋¹⁺²	1	2	yes	—
12	C₂₄₁	C₃²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²⋊C₉	C₂₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³	C₃×C₂₄₁	1	1	yes	characteristic
15	C₃×C₉	C₃×C₂₄₁	1	3	yes	complemented
16	C₃²	—	3	1	no	—
17	C₃²	—	3	2	no	—
18	C₃²	C₉×C₂₄₁	1	3	yes	complemented
19	C₃²	C₃²×C₂₄₁	1	1	yes	characteristic
20	C₉	—	3	3	no	—
21	C₃	—	3	3	no	—
22	C₃	C₃×C₉×C₂₄₁	1	1	yes	characteristic
23	C₃	H(3,𝔽₃)×C₂₄₁	1	1	yes	characteristic
24	C₃	3₋¹⁺²×C₂₄₁	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.