Subgroups — A₄×3₋¹⁺² #66439

Order 324.

84 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	C₂²×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
3	#1094	C₃	1	2	yes	maximal, complemented
4	C₉⋊A₄	C₃	1	6	yes	maximal, complemented
5	C₉×A₄	C₃	1	3	yes	maximal, complemented
6	C₃×3₋¹⁺²	—	4	1	no	maximal, Sylow
7	C₂×3₋¹⁺²	—	3	1	no	—
8	C₂²×C₃²	C₃²	1	1	yes	characteristic
9	C₃×A₄	—	3	3	no	—
10	C₃×A₄	C₃²	1	2	yes	—
11	C₃×A₄	C₃²	1	1	yes	characteristic
12	C₂²×C₉	C₃²	1	3	yes	complemented
13	C₂²⋊C₉	C₃²	1	6	yes	complemented
14	C₃³	—	4	1	no	—
15	3₋¹⁺²	—	4	2	no	—
16	3₋¹⁺²	—	4	6	no	—
17	3₋¹⁺²	A₄	1	1	yes	characteristic, direct product factor
18	C₃×C₉	—	4	3	no	—
19	C₂×C₃²	—	3	1	no	—
20	C₂×C₉	—	3	3	no	—
21	C₂²×C₃	—	3	1	no	—
22	C₂²×C₃	C₃³	1	1	yes	characteristic
23	A₄	—	3	2	no	—
24	A₄	3₋¹⁺²	1	3	yes	direct product factor
25	C₃²	—	4	1	no	—
26	C₃²	—	4	2	no	—
27	C₃²	—	12	3	no	—
28	C₃²	C₃×A₄	1	1	yes	characteristic
29	C₉	—	4	6	no	—
30	C₉	C₃×A₄	1	3	yes	complemented
31	C₂×C₃	—	3	1	no	—
32	C₂×C₃	—	9	1	no	—
33	C₂²	C₃×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
34	C₃	—	3	1	no	—
35	C₃	—	4	3	no	—
36	C₃	—	12	2	no	—
37	C₃	C₃²×A₄	1	1	yes	characteristic
38	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.