Subgroups — #88863

Order 432.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₈	C₂	1	1	yes	maximal, characteristic
2	#6308	C₂	1	1	yes	maximal, characteristic
3	C₃⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic
4	#3756	—	3	13	no	maximal
5	C₃³×C₄	—	2	1	no	—
6	C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
8	C₃²×Q₈	D₃	1	13	yes	—
9	#634	—	3	13	no	—
10	C₃⋊(C₃⋊C₈)	—	3	13	no	—
11	C₂×C₃³	D₄	1	1	yes	characteristic
12	#216	—	9	13	no	—
13	C₃²×C₄	—	2	13	no	—
14	C₃²×C₄	C₂×D₃	1	13	yes	—
15	C₃⋊Dic₃	—	6	13	no	—
16	C₃³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
17	C₃×Q₈	C₃⋊D₃	1	13	yes	—
18	Dic₆	—	9	13	no	—
19	C₃⋊C₈	—	9	13	no	—
20	C₂×C₃²	#67	1	13	yes	—
21	Q₁₆	—	27	1	no	Sylow
22	C₃×C₄	—	2	13	no	—
23	C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
24	Dic₃	—	18	13	no	—
25	C₃²	#216	1	13	yes	complemented
26	Q₈	—	27	1	no	—
27	Q₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
28	C₈	—	27	1	no	—
29	C₂×C₃	#638	1	13	yes	—
30	C₄	—	2	1	no	—
31	C₄	—	54	1	no	—
32	C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
33	C₃	#3756	1	13	yes	complemented
34	C₂	#6312	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.