Subgroups — C₄×C₃⋊(C₃⋊Dic₃) #88856

Order 432.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊(C₃⋊Dic₃)	C₂	1	2	yes	maximal
3	C₄×C₃⋊Dic₃	—	3	13	no	maximal
4	C₂²×C₃³	C₂²	1	1	yes	characteristic
5	C₃³×C₄	C₄	1	2	yes	complemented
6	C₃⋊(C₃⋊Dic₃)	C₄	1	4	yes	direct product factor
7	C₂×C₃²×C₄	D₃	1	13	yes	—
8	C₂×C₃⋊Dic₃	—	3	26	no	—
9	C₂×C₃³	C₂×C₄	1	2	yes	—
10	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
11	C₄×Dic₃	—	9	13	no	—
12	C₂²×C₃²	C₂×D₃	1	13	yes	—
13	C₃²×C₄	Dic₃	1	26	yes	complemented
14	C₃⋊Dic₃	—	3	52	no	—
15	C₃³	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₄	C₃⋊D₃	1	13	yes	—
17	C₂×Dic₃	—	9	26	no	—
18	C₂×C₃²	C₄×D₃	1	26	yes	—
19	C₂×C₃²	C₂×Dic₃	1	13	yes	—
20	C₄²	—	27	1	no	Sylow
21	C₂²×C₃	C₂×C₃⋊D₃	1	13	yes	—
22	C₃×C₄	C₃⋊Dic₃	1	26	yes	complemented
23	Dic₃	—	9	52	no	—
24	C₃²	C₄×Dic₃	1	13	yes	complemented
25	C₂×C₄	—	27	2	no	—
26	C₂×C₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
27	C₂×C₃	C₄×C₃⋊D₃	1	26	yes	—
28	C₂×C₃	C₂×C₃⋊Dic₃	1	13	yes	—
29	C₂²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
30	C₄	—	27	4	no	—
31	C₄	C₃⋊(C₃⋊Dic₃)	1	2	yes	direct product factor
32	C₃	C₄×C₃⋊Dic₃	1	13	yes	complemented
33	C₂	C₄×C₃⋊(C₃⋊D₃)	1	2	yes	—
34	C₂	C₂×C₃⋊(C₃⋊Dic₃)	1	1	yes	characteristic

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.