Subgroups — C₂²×C₃⋊(C₃⋊Dic₃) #89081

Order 432.

756 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊(C₃⋊Dic₃)	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃⋊Dic₃	—	3	13	no	maximal
4	C₂²×C₃³	C₄	1	4	yes	complemented
5	C₂²×C₃³	C₂²	1	3	yes	—
6	C₃⋊(C₃⋊Dic₃)	C₂²	1	4	yes	direct product factor
7	C₂³×C₃²	D₃	1	13	yes	—
8	C₂×C₃⋊Dic₃	—	3	78	no	—
9	C₂×C₃³	C₂×C₄	1	6	yes	complemented
10	C₂×C₃³	C₂³	1	1	yes	characteristic
11	C₂²×Dic₃	—	9	13	no	—
12	C₂²×C₃²	Dic₃	1	52	yes	complemented
13	C₂²×C₃²	C₂×D₃	1	39	yes	—
14	C₃⋊Dic₃	—	3	52	no	—
15	C₃³	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂³×C₃	C₃⋊D₃	1	13	yes	—
17	C₂×Dic₃	—	9	78	no	—
18	C₂×C₃²	C₂×Dic₃	1	78	yes	complemented
19	C₂×C₃²	C₂²×D₃	1	13	yes	—
20	C₂²×C₄	—	27	1	no	Sylow
21	C₂²×C₃	C₃⋊Dic₃	1	52	yes	complemented
22	C₂²×C₃	C₂×C₃⋊D₃	1	39	yes	—
23	Dic₃	—	9	52	no	—
24	C₃²	C₂²×Dic₃	1	13	yes	complemented
25	C₂³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
26	C₂×C₄	—	27	6	no	—
27	C₂×C₃	C₂×C₃⋊Dic₃	1	78	yes	complemented
28	C₂×C₃	C₂²×C₃⋊D₃	1	13	yes	—
29	C₂²	C₃⋊(C₃⋊Dic₃)	1	4	yes	direct product factor
30	C₂²	C₂×C₃⋊(C₃⋊D₃)	1	3	yes	—
31	C₄	—	27	4	no	—
32	C₃	C₂²×C₃⋊Dic₃	1	13	yes	complemented
33	C₂	C₂×C₃⋊(C₃⋊Dic₃)	1	6	yes	direct product factor
34	C₂	C₂²×C₃⋊(C₃⋊D₃)	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.