Subgroups — #6249⋊C₂ #88873

Order 432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	SU(3,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	#1088⋊C₂	C₂	1	1	yes	maximal, characteristic
3	#6249	C₂	1	1	yes	maximal, characteristic, complemented
4	((C₃⋊D₃)⋊C₃)⋊C₂	—	2	1	no	—
5	#1088	—	2	1	no	—
6	#1088	C₂²	1	1	yes	characteristic
7	#272	D₄	1	1	yes	characteristic
8	(C₃⋊D₃)⋊C₃	—	4	1	no	—
9	#215	—	9	1	no	maximal
10	D₃²	—	12	1	no	—
11	H(3,𝔽₃)	SD₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₃×Q₈	—	9	1	no	—
13	D₁₂	—	9	1	no	—
14	C₃⋊C₈	—	9	1	no	—
15	C₃⋊D₃	—	4	1	no	—
16	C₃×D₃	—	12	1	no	—
17	C₃×D₃	—	12	1	no	—
18	SD₁₆	—	27	1	no	Sylow
19	C₂×D₃	—	18	1	no	—
20	C₂×D₃	—	36	1	no	—
21	C₃×C₄	—	9	1	no	—
22	C₃×C₄	—	18	1	no	—
23	C₃²	—	4	1	no	—
24	Q₈	—	9	1	no	—
25	D₄	—	27	1	no	—
26	C₈	—	27	1	no	—
27	C₂×C₃	—	9	1	no	—
28	C₂×C₃	—	36	1	no	—
29	D₃	—	12	1	no	—
30	D₃	—	12	1	no	—
31	D₃	—	36	1	no	—
32	C₂²	—	54	1	no	—
33	C₄	—	9	1	no	—
34	C₄	—	18	1	no	—
35	C₃	—	12	1	no	—
36	C₃	AΓL(1,𝔽₉)	1	1	yes	characteristic
37	C₂	—	9	1	no	—
38	C₂	—	36	1	no	—

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.