Subgroups — #88864

Order 432.

476 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	2	yes	maximal, complemented
3	#3757	—	3	13	no	maximal
4	C₂²×C₃³	—	2	2	no	—
5	C₂²×C₃³	C₄	1	2	yes	complemented
6	C₂²×C₃³	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
8	C₂³×C₃²	D₃	1	13	yes	—
9	C₂×C₃⋊Dic₃	—	3	26	no	—
10	C₂×C₃³	—	2	2	no	—
11	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃³	D₄	1	2	yes	—
13	#217	—	9	13	no	—
14	C₂²×C₃²	—	2	26	no	—
15	C₂²×C₃²	Dic₃	1	26	yes	complemented
16	C₂²×C₃²	C₂×D₃	1	13	yes	—
17	C₃⋊Dic₃	—	6	26	no	—
18	C₃³	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₃	C₃⋊D₃	1	13	yes	—
20	C₂×Dic₃	—	9	26	no	—
21	C₂×C₃²	—	2	26	no	—
22	C₂×C₃²	C₂×Dic₃	1	13	yes	—
23	C₂×C₃²	#67	1	26	yes	—
24	C₂²⋊C₄	—	27	1	no	Sylow
25	C₂²×C₃	—	2	26	no	—
26	C₂²×C₃	C₃⋊Dic₃	1	26	yes	complemented
27	C₂²×C₃	C₂×C₃⋊D₃	1	13	yes	—
28	Dic₃	—	18	26	no	—
29	C₃²	#217	1	13	yes	complemented
30	C₂³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
31	C₂×C₄	—	27	2	no	—
32	C₂×C₃	—	2	26	no	—
33	C₂×C₃	C₂×C₃⋊Dic₃	1	13	yes	—
34	C₂×C₃	#638	1	26	yes	—
35	C₂²	—	2	2	no	—
36	C₂²	C₃⋊(C₃⋊Dic₃)	1	2	yes	complemented
37	C₂²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
38	C₄	—	54	2	no	—
39	C₃	#3757	1	13	yes	complemented
40	C₂	—	2	2	no	—
41	C₂	C₂×C₃⋊(C₃⋊Dic₃)	1	1	yes	characteristic
42	C₂	#6312	1	2	yes	—

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.