Subgroups — C₄×#13064104 #19150577

Order 5628.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13064104	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#13064104	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₄×C₆₇⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₆₇⋊C₃	—	7	1	no	—
8	C₄×C₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	C₆₇⋊C₃	—	7	1	no	Hall
10	C₂×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₄×ΓL(1,𝔽₈)	—	67	1	no	maximal, Hall
12	C₆₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
13	C₂×ΓL(1,𝔽₈)	—	67	1	no	—
14	C₄×C₇	C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₈)	—	67	1	no	Hall
16	C₂×C₇	C₂×C₆₇⋊C₃	1	1	yes	characteristic
17	C₃×C₄	—	469	1	no	Hall
18	C₇	C₄×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	469	1	no	—
20	C₄	#13064104	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	469	1	no	Sylow
22	C₂	C₂×#13064104	1	1	yes	characteristic

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