Subgroups — C₉⋊(C₂²⋊C₉) #66356

Order 324.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊C₉	C₃	1	3	yes	maximal
3	C₉⋊C₉	—	4	1	no	maximal, Sylow
4	C₂×C₃×C₉	—	3	1	no	—
5	C₂²×C₃²	C₃²	1	1	yes	characteristic
6	C₂²×C₉	C₉	1	3	yes	complemented
7	C₂²⋊C₉	—	3	3	no	—
8	C₃×C₉	—	4	3	no	—
9	C₃×C₉	A₄	1	1	yes	characteristic
10	C₂×C₃²	—	3	1	no	—
11	C₂×C₉	—	3	3	no	—
12	C₂²×C₃	C₃×C₉	1	1	yes	characteristic
13	C₂²×C₃	3₋¹⁺²	1	3	yes	—
14	C₃²	C₃×A₄	1	1	yes	characteristic
15	C₉	—	12	3	no	—
16	C₉	C₂²⋊C₉	1	3	yes	complemented
17	C₂×C₃	—	3	3	no	—
18	C₂×C₃	—	3	1	no	—
19	C₂²	C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₃	C₉⋊A₄	1	3	yes	—
21	C₃	C₃×C₂²⋊C₉	1	1	yes	characteristic
22	C₂	—	3	1	no	—

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.