Subgroups — C₃×SL(2,𝔽₈) #13094883

Order 1512.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	SL(2,𝔽₈)	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×AGL(1,𝔽₈)	—	9	1	no	maximal
3	AGL(1,𝔽₈)	—	9	1	no	Hall
4	C₃×D₉	—	28	1	no	maximal
5	C₃×D₇	—	36	1	no	maximal
6	C₃×C₉	—	28	1	no	Sylow
7	C₂³×C₃	—	9	1	no	—
8	C₃×C₇	—	36	1	no	—
9	C₃×D₃	—	84	1	no	—
10	D₉	—	28	1	no	—
11	D₇	—	36	1	no	—
12	C₂²×C₃	—	63	1	no	—
13	C₃²	—	28	1	no	—
14	C₉	—	28	1	no	—
15	C₉	—	56	1	no	—
16	C₂³	—	9	1	no	Sylow
17	C₇	—	36	1	no	Sylow
18	C₂×C₃	—	63	1	no	—
19	D₃	—	84	1	no	—
20	C₂²	—	63	1	no	—
21	C₃	—	28	1	no	—
22	C₃	—	56	1	no	—
23	C₃	SL(2,𝔽₈)	1	1	yes	maximal normal, characteristic, direct product factor
24	C₂	—	63	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. SL(2,𝔽₈)	C₃	direct (N × H)
23. C₃	SL(2,𝔽₈)	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.