Subgroups — C₃×#14584195 #22554751

Order 8442.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13064105	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#14584195	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
5	#13064105	C₂×C₃	1	3	yes	complemented
6	C₃×D₆₇⋊C₃	—	7	1	no	maximal, Hall
7	C₇×D₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₆₇⋊C₃	—	7	1	no	Hall
9	C₇×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	D₆₇⋊C₃	—	7	3	no	—
12	C₃×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₆₇⋊C₃	—	7	3	no	—
14	D₆₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×ΓL(1,𝔽₈)	—	67	1	no	maximal, Hall
16	C₆₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
17	C₃×ΓL(1,𝔽₈)	—	67	1	no	Hall
18	C₂×C₃×C₇	—	67	1	no	—
19	C₂×ΓL(1,𝔽₈)	—	67	3	no	—
20	C₃×C₇	D₆₇⋊C₃	1	1	yes	characteristic, complemented
21	ΓL(1,𝔽₈)	—	67	3	no	—
22	C₂×C₃²	—	469	1	no	Hall
23	C₂×C₇	—	67	1	no	Hall
24	C₃²	—	469	1	no	Sylow
25	C₇	C₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	67	1	no	—
27	C₂×C₃	—	469	3	no	—
28	C₃	—	469	3	no	—
29	C₃	#14584195	1	1	yes	characteristic, direct product factor
30	C₂	—	67	1	no	Sylow

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