Subgroups — C₁₇×C₃⋊#10621721 #46828152

Order 34476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₆₉	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#10621721	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₁₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₁₆₉	D₃	1	1	yes	characteristic
5	C₁₇×C₁₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₁₇×C₃⋊#261	—	13	1	no	maximal
7	C₃⋊#10621721	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₇×D₁₃	—	13	1	no	—
9	C₃×D₁₆₉	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×#261	—	39	1	no	—
11	#10621721	—	3	1	no	Hall
12	C₃×C₁₃×C₁₇	#261	1	1	yes	characteristic
13	C₃×C₁₆₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₁₇×D₁₃	—	13	1	no	—
15	D₁₆₉	D₃×C₁₇	1	1	yes	characteristic
16	C₁₃×C₁₇	C₃⋊#261	1	1	yes	characteristic
17	Dic₃×C₁₇	—	169	1	no	Hall
18	C₁₆₉	Dic₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
19	C₃⋊#261	—	13	1	no	—
20	C₂×C₃×C₁₇	—	169	1	no	—
21	C₃×D₁₃	—	13	1	no	—
22	C₄×C₁₇	—	507	1	no	Hall
23	#261	—	39	1	no	—
24	C₃×C₁₇	#10621721	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₃	C₁₇×#261	1	1	yes	characteristic
26	C₂×C₁₇	—	169	1	no	—
27	D₁₃	—	13	1	no	—
28	C₁₇	C₃⋊#10621721	1	1	yes	characteristic, direct product factor, Sylow
29	C₁₃	C₁₇×C₃⋊#261	1	1	yes	characteristic
30	Dic₃	—	169	1	no	Hall
31	C₂×C₃	—	169	1	no	—
32	C₄	—	507	1	no	Sylow
33	C₃	C₁₇×#10621721	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	169	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.