Subgroups — #88855

Order 432.

280 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	C₃⋊(C₃⋊(C₃⋊C₈))	C₂	1	2	yes	maximal, complemented
3	#3748	—	3	13	no	maximal
4	C₂²×C₃³	C₄	1	1	yes	characteristic
5	C₃³×C₄	C₄	1	1	yes	characteristic
6	C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄	D₃	1	13	yes	—
8	C₃⋊(C₃⋊C₈)	—	3	26	no	—
9	C₂×C₃³	—	2	1	no	—
10	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
11	#208	—	9	13	no	—
12	C₂²×C₃²	Dic₃	1	13	yes	—
13	C₃²×C₄	Dic₃	1	13	yes	—
14	C₃²×C₄	C₂×D₃	1	13	yes	—
15	C₃³	M₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₄	C₃⋊D₃	1	13	yes	—
17	C₃⋊C₈	—	9	26	no	—
18	C₂×C₃²	—	2	13	no	—
19	C₂×C₃²	C₂×Dic₃	1	13	yes	—
20	M₁₆	—	27	1	no	Sylow
21	C₂²×C₃	C₃⋊Dic₃	1	13	yes	—
22	C₃×C₄	C₃⋊Dic₃	1	13	yes	—
23	C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
24	C₃²	#208	1	13	yes	complemented
25	C₂×C₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
26	C₈	—	27	2	no	—
27	C₂×C₃	—	2	13	no	—
28	C₂×C₃	C₂×C₃⋊Dic₃	1	13	yes	—
29	C₂²	C₃⋊(C₃⋊Dic₃)	1	1	yes	characteristic
30	C₄	C₃⋊(C₃⋊Dic₃)	1	1	yes	characteristic
31	C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
32	C₃	#3748	1	13	yes	complemented
33	C₂	—	2	1	no	—
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.