Subgroups — C₁₇×#11717941 #28358193

Order 13923.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₁₇	C₃	1	1	yes	maximal, characteristic
2	C₁₇×C₁₃⋊C₉	—	7	1	no	maximal, Hall
3	C₇×C₁₃×C₁₇	C₉	1	1	yes	characteristic, complemented, Hall
4	C₁₇×C₇⋊C₉	—	13	1	no	maximal, Hall
5	#11717941	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₁₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₃×C₇×C₁₇	C₁₃⋊C₃	1	1	yes	characteristic
8	C₃×C₇×C₁₃	C₃×C₁₇	1	1	yes	characteristic
9	C₁₃×C₁₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
10	C₉×C₁₇	—	91	1	no	Hall
11	C₇×C₁₇	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₁₃⋊C₉	—	7	1	no	Hall
13	C₇×C₁₃	C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₇⋊C₉	—	13	1	no	Hall
15	C₃×C₁₇	#63270	1	1	yes	characteristic
16	C₃×C₁₃	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₃×C₇	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic
18	C₁₇	#11717941	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	C₁₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₉	—	91	1	no	Sylow
21	C₇	C₁₇×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
22	C₃	C₁₇×#63270	1	1	yes	characteristic

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.