Subgroups — C₃²⋊(C₄²⋊C₃) #88456

Order 432.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄²	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄²⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₂²⋊H(3,𝔽₃)	—	4	1	no	maximal
4	C₂×C₃²×C₄	—	3	1	no	—
5	C₃×C₄²	—	3	1	no	—
6	C₃×C₄²	C₃²	1	1	yes	characteristic
7	C₄²⋊C₃	—	3	3	no	—
8	C₂²×C₃²	A₄	1	1	yes	characteristic
9	C₃×A₄	—	4	3	no	—
10	C₃²×C₄	—	3	2	no	—
11	H(3,𝔽₃)	—	16	1	no	Sylow
12	C₂×C₃×C₄	—	3	3	no	—
13	C₂×C₃×C₄	—	3	1	no	—
14	C₂×C₃²	—	3	1	no	—
15	C₄²	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃	—	3	1	no	—
17	C₂²×C₃	C₃×A₄	1	1	yes	characteristic
18	A₄	—	12	3	no	—
19	C₃×C₄	—	3	6	no	—
20	C₃×C₄	—	3	2	no	—
21	C₃²	—	16	3	no	—
22	C₃²	C₄²⋊C₃	1	1	yes	characteristic, complemented
23	C₂×C₄	—	3	1	no	—
24	C₂×C₃	—	3	3	no	—
25	C₂×C₃	—	3	1	no	—
26	C₂²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
27	C₄	—	3	2	no	—
28	C₃	—	3	1	no	—
29	C₃	—	48	3	no	—
30	C₃	C₃×C₄²⋊C₃	1	1	yes	characteristic
31	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.