Subgroups — C₉⋊(C₂²⋊A₄) #88905

Order 432.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊A₄	C₃	1	1	yes	maximal, characteristic
2	C₂⁴×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₂²⋊C₉)	C₃	1	2	yes	maximal, complemented
4	C₉⋊A₄	—	4	5	no	maximal
5	C₂³×C₉	—	3	5	no	—
6	C₂⁴×C₃	C₃²	1	1	yes	characteristic
7	C₂²⋊A₄	—	3	1	no	—
8	C₃×A₄	—	4	5	no	—
9	C₂²×C₉	—	3	10	no	—
10	C₂²×C₉	A₄	1	5	yes	complemented
11	C₂²⋊C₉	—	4	10	no	—
12	3₋¹⁺²	—	16	1	no	Sylow
13	C₂³×C₃	—	3	5	no	—
14	C₂×C₉	—	3	5	no	—
15	C₂⁴	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃	—	3	10	no	—
17	C₂²×C₃	C₃×A₄	1	5	yes	—
18	A₄	—	12	5	no	—
19	C₃²	—	16	1	no	—
20	C₉	—	16	2	no	—
21	C₉	C₂²⋊A₄	1	1	yes	characteristic, complemented
22	C₂³	—	3	5	no	—
23	C₂×C₃	—	3	5	no	—
24	C₂²	—	3	10	no	—
25	C₂²	C₉⋊A₄	1	5	yes	complemented
26	C₃	—	48	1	no	—
27	C₃	C₃×C₂²⋊A₄	1	1	yes	characteristic
28	C₂	—	3	5	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.