Subgroups — C₉×C₄²⋊C₃ #88452

Order 432.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₄²×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄²⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₉×A₄	—	4	1	no	maximal
5	C₂×C₄×C₉	—	3	1	no	—
6	C₃×C₄²	C₃²	1	1	yes	characteristic
7	C₄²⋊C₃	C₉	1	3	yes	direct product factor
8	C₃×A₄	—	4	1	no	—
9	C₂²×C₉	A₄	1	1	yes	characteristic
10	C₂²⋊C₉	—	4	2	no	—
11	C₄×C₉	—	3	2	no	—
12	C₃×C₉	—	16	1	no	Sylow
13	C₂×C₃×C₄	—	3	1	no	—
14	C₂×C₉	—	3	1	no	—
15	C₄²	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃	C₃×A₄	1	1	yes	characteristic
17	A₄	—	4	3	no	—
18	C₃×C₄	—	3	2	no	—
19	C₃²	—	16	1	no	—
20	C₉	—	16	2	no	—
21	C₉	C₄²⋊C₃	1	1	yes	characteristic, direct product factor
22	C₂×C₄	—	3	1	no	—
23	C₂×C₃	—	3	1	no	—
24	C₂²	C₉×A₄	1	1	yes	characteristic
25	C₄	—	3	2	no	—
26	C₃	—	16	3	no	—
27	C₃	C₃×C₄²⋊C₃	1	1	yes	characteristic
28	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.