Subgroups — C₉⋊(C₂²⋊(C₂²⋊A₄)) #13180114

Order 1728.

3133 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊(C₂²⋊A₄)	C₃	1	1	yes	maximal, characteristic
2	C₂⁶×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₂²⋊(C₂²⋊C₉))	C₃	1	2	yes	maximal, complemented
4	C₉⋊(C₂²⋊A₄)	—	4	21	no	maximal
5	C₂⁵×C₉	—	3	21	no	—
6	C₂⁶×C₃	C₃²	1	1	yes	characteristic
7	C₂²⋊(C₂²⋊A₄)	—	3	1	no	—
8	C₃×C₂²⋊A₄	—	4	21	no	—
9	C₂⁴×C₉	—	3	210	no	—
10	C₂⁴×C₉	A₄	1	21	yes	complemented
11	C₂²⋊(C₂²⋊C₉)	—	4	42	no	—
12	C₉⋊A₄	—	16	21	no	—
13	C₂⁵×C₃	—	3	21	no	—
14	C₂³×C₉	—	3	360	no	—
15	C₂³×C₉	—	3	105	no	—
16	C₂⁶	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
17	C₂⁴×C₃	—	3	210	no	—
18	C₂⁴×C₃	C₃×A₄	1	21	yes	—
19	C₂²⋊A₄	—	12	21	no	—
20	C₃×A₄	—	16	21	no	—
21	C₂²×C₉	—	3	210	no	—
22	C₂²×C₉	C₂²⋊A₄	1	21	yes	complemented
23	C₂²⋊C₉	—	16	42	no	—
24	C₂⁵	—	3	21	no	—
25	3₋¹⁺²	—	64	1	no	Sylow
26	C₂³×C₃	—	3	360	no	—
27	C₂³×C₃	—	3	105	no	—
28	C₂×C₉	—	3	21	no	—
29	C₂⁴	—	3	210	no	—
30	C₂⁴	C₉⋊A₄	1	21	yes	complemented
31	C₂²×C₃	—	3	210	no	—
32	C₂²×C₃	C₃×C₂²⋊A₄	1	21	yes	—
33	A₄	—	48	21	no	—
34	C₃²	—	64	1	no	—
35	C₉	—	64	2	no	—
36	C₉	C₂²⋊(C₂²⋊A₄)	1	1	yes	characteristic, complemented
37	C₂³	—	3	360	no	—
38	C₂³	—	3	105	no	—
39	C₂×C₃	—	3	21	no	—
40	C₂²	—	3	210	no	—
41	C₂²	C₉⋊(C₂²⋊A₄)	1	21	yes	complemented
42	C₃	—	192	1	no	—
43	C₃	C₃×C₂²⋊(C₂²⋊A₄)	1	1	yes	characteristic
44	C₂	—	3	21	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.