Subgroups — C₁₇×C₃⋊#4223 #22552575

Order 8364.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#4223	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₄₁	D₃	1	1	yes	characteristic
5	C₁₇×C₄₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#4223	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×D₄₁	C₂×C₁₇	1	1	yes	characteristic
8	Dic₃×C₁₇	—	41	1	no	maximal, Hall
9	#4223	—	3	1	no	Hall
10	C₃×C₄₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₇	—	41	1	no	—
12	D₄₁	D₃×C₁₇	1	1	yes	characteristic
13	C₄×C₁₇	—	123	1	no	Hall
14	C₃×C₁₇	#4223	1	1	yes	characteristic, complemented, Hall
15	C₄₁	Dic₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₇	—	41	1	no	—
17	C₁₇	C₃⋊#4223	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₃	—	41	1	no	Hall
19	C₂×C₃	—	41	1	no	—
20	C₄	—	123	1	no	Sylow
21	C₃	C₁₇×#4223	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	41	1	no	—

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