Subgroups — Dic₅₅₁₇ #36348158

Order 22068.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₆₁₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₈₃₉	—	3	1	no	maximal
3	C₉×C₆₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₆₁₃	D₃	1	1	yes	characteristic
5	Dic₆₁₃	—	9	1	no	Hall
6	C₃×C₆₁₃	Dic₃	1	1	yes	characteristic
7	C₂×C₆₁₃	D₉	1	1	yes	characteristic
8	C₆₁₃	Dic₉	1	1	yes	characteristic, complemented, Sylow
9	Dic₉	—	613	1	no	maximal, Hall
10	C₂×C₉	D₆₁₃	1	1	yes	characteristic
11	Dic₃	—	1839	1	no	—
12	C₉	Dic₆₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃	D₁₈₃₉	1	1	yes	characteristic
14	C₄	—	5517	1	no	Sylow
15	C₃	Dic₁₈₃₉	1	1	yes	characteristic
16	C₂	D₅₅₁₇	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.