Subgroups — #88853

Order 432.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6308	C₂	1	2	yes	maximal
2	C₃³×C₈	C₂	1	1	yes	maximal, characteristic
3	#3746	—	3	13	no	maximal
4	C₃³×C₄	C₂²	1	1	yes	characteristic
5	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
6	#634	—	3	26	no	—
7	C₃²×C₈	D₃	1	13	yes	—
8	C₂×C₃³	D₄	1	1	yes	characteristic
9	Dic₁₂	—	9	13	no	—
10	C₃²×C₄	C₂×D₃	1	13	yes	—
11	C₃⋊Dic₃	—	6	26	no	—
12	C₃³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
13	Dic₆	—	9	26	no	—
14	C₃×C₈	C₃⋊D₃	1	13	yes	—
15	C₂×C₃²	D₁₂	1	13	yes	—
16	Q₁₆	—	27	1	no	Sylow
17	C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
18	Dic₃	—	18	26	no	—
19	C₃²	Dic₁₂	1	13	yes	complemented
20	Q₈	—	27	2	no	—
21	C₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
22	C₂×C₃	C₄⋊(C₃⋊D₃)	1	13	yes	—
23	C₄	—	54	2	no	—
24	C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
25	C₃	#3746	1	13	yes	complemented
26	C₂	C₄⋊(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.