Subgroups — Dic₇₆₀₈ #72272002

Order 30432.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₈₀₄	C₂	1	2	yes	maximal
2	Dic₁₉₀₂	—	2	2	no	—
3	C₃×C₁₆×C₃₁₇	C₂	1	1	yes	maximal, characteristic
4	C₃×C₈×C₃₁₇	C₂²	1	1	yes	characteristic
5	Dic₂₅₃₆	—	3	1	no	maximal, Hall
6	Dic₁₂₆₈	—	3	2	no	—
7	C₁₆×C₃₁₇	D₃	1	1	yes	characteristic
8	Dic₉₅₁	—	4	2	no	—
9	C₃×C₄×C₃₁₇	D₄	1	1	yes	characteristic
10	Dic₆₃₄	—	6	2	no	—
11	C₈×C₃₁₇	C₂×D₃	1	1	yes	characteristic
12	C₂×C₃×C₃₁₇	D₈	1	1	yes	characteristic
13	C₄×C₃₁₇	D₁₂	1	1	yes	characteristic
14	Dic₃₁₇	—	12	2	no	—
15	C₃×C₃₁₇	Q₃₂	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₁₇	D₂₄	1	1	yes	characteristic
17	C₃₁₇	Dic₂₄	1	1	yes	characteristic, complemented, Sylow
18	Dic₂₄	—	317	1	no	maximal, Hall
19	Dic₁₂	—	317	2	no	—
20	C₃×C₁₆	D₃₁₇	1	1	yes	characteristic
21	Q₃₂	—	951	1	no	Sylow
22	Dic₆	—	634	2	no	—
23	C₃×C₈	C₂×D₃₁₇	1	1	yes	characteristic
24	Q₁₆	—	951	2	no	—
25	C₁₆	D₉₅₁	1	1	yes	characteristic
26	C₃×C₄	D₁₂₆₈	1	1	yes	characteristic
27	Dic₃	—	1268	2	no	—
28	Q₈	—	1902	2	no	—
29	C₈	C₂×D₉₅₁	1	1	yes	characteristic
30	C₂×C₃	D₂₅₃₆	1	1	yes	characteristic
31	C₄	—	3804	2	no	—
32	C₄	D₃₈₀₄	1	1	yes	characteristic
33	C₃	Dic₂₅₃₆	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₇₆₀₈	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.