Subgroups — C₃²⋊(C₂²⋊C₉) #66367

Order 324.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³	C₃	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₃²⋊C₉	—	4	1	no	maximal, Sylow
4	C₂×C₃³	—	3	1	no	—
5	C₂²×C₃²	—	3	1	no	—
6	C₂²×C₃²	—	3	2	no	—
7	C₂²×C₃²	C₉	1	3	yes	complemented
8	C₂²×C₃²	C₃²	1	1	yes	characteristic
9	C₂²⋊C₉	—	3	3	no	—
10	C₃³	A₄	1	1	yes	characteristic
11	C₃×C₉	—	4	3	no	—
12	C₂×C₃²	—	3	6	no	—
13	C₂×C₃²	—	3	3	no	—
14	C₂×C₃²	—	3	3	no	—
15	C₂×C₃²	—	3	1	no	—
16	C₂²×C₃	—	3	3	no	—
17	C₂²×C₃	C₃×C₉	1	1	yes	characteristic
18	C₂²×C₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₂²×C₃	3₋¹⁺²	1	2	yes	—
20	C₃²	—	3	2	no	—
21	C₃²	—	3	1	no	—
22	C₃²	C₂²⋊C₉	1	3	yes	complemented
23	C₃²	C₃×A₄	1	1	yes	characteristic
24	C₉	—	12	3	no	—
25	C₂×C₃	—	3	9	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	—	3	2	no	—
28	C₂×C₃	—	3	1	no	—
29	C₂²	C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
30	C₃	—	3	3	no	—
31	C₃	C₃×C₂²⋊C₉	1	1	yes	characteristic
32	C₃	#1094	1	2	yes	—
33	C₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
34	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.