Subgroups — Dic₆₈₆₇ #42117331

Order 27468.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₂₈₉	—	3	1	no	maximal
3	C₇×C₉×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₀₉	D₃	1	1	yes	characteristic
5	Dic₉₈₁	—	7	1	no	maximal, Hall
6	Dic₇₆₃	—	9	1	no	Hall
7	C₃×C₇×C₁₀₉	Dic₃	1	1	yes	characteristic
8	C₂×C₉×C₁₀₉	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₀₉	D₉	1	1	yes	characteristic
10	Dic₃₂₇	—	21	1	no	—
11	C₉×C₁₀₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₀₉	Dic₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₀₉	D₂₁	1	1	yes	characteristic
14	Dic₁₀₉	—	63	1	no	Hall
15	C₃×C₁₀₉	Dic₂₁	1	1	yes	characteristic
16	Dic₆₃	—	109	1	no	maximal, Hall
17	C₂×C₁₀₉	D₆₃	1	1	yes	characteristic
18	C₂×C₇×C₉	D₁₀₉	1	1	yes	characteristic
19	C₁₀₉	Dic₆₃	1	1	yes	characteristic, complemented, Sylow
20	Dic₂₁	—	327	1	no	—
21	C₇×C₉	Dic₁₀₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₃₂₇	1	1	yes	characteristic
23	Dic₉	—	763	1	no	Hall
24	Dic₇	—	981	1	no	Hall
25	C₃×C₇	Dic₃₂₇	1	1	yes	characteristic
26	C₂×C₉	D₇₆₃	1	1	yes	characteristic
27	C₂×C₇	D₉₈₁	1	1	yes	characteristic
28	Dic₃	—	2289	1	no	—
29	C₉	Dic₇₆₃	1	1	yes	characteristic, complemented, Sylow
30	C₇	Dic₉₈₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₂₂₈₉	1	1	yes	characteristic
32	C₄	—	6867	1	no	Sylow
33	C₃	Dic₂₂₈₉	1	1	yes	characteristic
34	C₂	D₆₈₆₇	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.