Subgroups — C₂×C₉×A₄ #6266

Order 216.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×A₄	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₃×A₄	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₂×C₃×C₉	—	4	1	no	maximal
6	C₃×A₄	C₂×C₃	1	1	yes	characteristic
7	C₂²×C₉	—	3	1	no	—
8	C₂²×C₉	—	3	1	no	—
9	C₂²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂²⋊C₉	C₂×C₃	1	2	yes	complemented
11	C₃×C₉	—	4	1	no	Sylow
12	C₂³×C₃	C₃²	1	1	yes	characteristic
13	C₂×A₄	C₉	1	3	yes	direct product factor
14	C₂×C₃²	—	4	1	no	—
15	C₂×C₉	—	3	1	no	—
16	C₂×C₉	—	3	1	no	—
17	C₂×C₉	—	4	2	no	—
18	C₂×C₉	A₄	1	1	yes	characteristic, direct product factor
19	C₂²×C₃	—	3	1	no	—
20	C₂²×C₃	—	3	1	no	—
21	C₂²×C₃	C₂×C₃²	1	1	yes	characteristic
22	A₄	C₂×C₉	1	3	yes	direct product factor
23	C₃²	—	4	1	no	—
24	C₉	—	4	2	no	—
25	C₉	C₂×A₄	1	1	yes	characteristic, direct product factor
26	C₂³	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂×C₃	—	3	1	no	—
29	C₂×C₃	—	4	3	no	—
30	C₂×C₃	C₃×A₄	1	1	yes	characteristic
31	C₂²	—	3	1	no	—
32	C₂²	—	3	1	no	—
33	C₂²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
34	C₃	—	4	3	no	—
35	C₃	C₂×C₃×A₄	1	1	yes	characteristic
36	C₂	—	3	1	no	—
37	C₂	—	3	1	no	—
38	C₂	C₉×A₄	1	1	yes	characteristic, direct product factor

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.