Subgroups — (C₃×A₄)⋊C₉ #66360

Order 324.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×A₄	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂²⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃²⋊C₉	—	4	1	no	maximal, Sylow
5	C₂×C₃×C₉	—	3	1	no	—
6	C₂²×C₃²	C₃²	1	1	yes	characteristic
7	C₃×A₄	—	3	1	no	—
8	C₃×A₄	—	3	2	no	—
9	C₃×A₄	C₉	1	3	yes	complemented
10	C₂²×C₉	—	3	1	no	—
11	C₂²⋊C₉	—	3	2	no	—
12	C₃³	—	4	1	no	—
13	C₃×C₉	—	4	2	no	—
14	C₃×C₉	A₄	1	1	yes	characteristic, complemented
15	C₂×C₃²	—	3	1	no	—
16	C₂×C₉	—	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	A₄	—	3	3	no	—
21	C₃²	—	4	3	no	—
22	C₃²	—	12	2	no	—
23	C₃²	—	12	1	no	—
24	C₃²	C₃×A₄	1	1	yes	characteristic
25	C₉	—	3	1	no	—
26	C₉	—	12	2	no	—
27	C₂×C₃	—	3	1	no	—
28	C₂×C₃	—	3	2	no	—
29	C₂×C₃	—	3	1	no	—
30	C₂²	C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₃	—	12	3	no	—
32	C₃	C₉×A₄	1	1	yes	characteristic
33	C₃	C₉⋊A₄	1	2	yes	—
34	C₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
35	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.