Subgroups — Dic₇₆₈ #72210830

Order 3072.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₈₄	C₂	1	2	yes	maximal
2	Q₁₀₂₄	—	3	1	no	maximal, Sylow
3	C₃×C₅₁₂	C₂	1	1	yes	maximal, characteristic
4	Dic₁₉₂	—	2	2	no	—
5	C₃×C₂₅₆	C₂²	1	1	yes	characteristic
6	Q₅₁₂	—	3	2	no	—
7	C₅₁₂	D₃	1	1	yes	characteristic
8	Dic₉₆	—	4	2	no	—
9	C₃×C₁₂₈	D₄	1	1	yes	characteristic
10	Q₂₅₆	—	6	2	no	—
11	C₂₅₆	C₂×D₃	1	1	yes	characteristic
12	Dic₄₈	—	8	2	no	—
13	C₃×C₆₄	D₈	1	1	yes	characteristic
14	Q₁₂₈	—	12	2	no	—
15	C₁₂₈	D₁₂	1	1	yes	characteristic
16	Dic₂₄	—	16	2	no	—
17	C₃×C₃₂	D₁₆	1	1	yes	characteristic
18	Q₆₄	—	24	2	no	—
19	C₆₄	D₂₄	1	1	yes	characteristic
20	Dic₁₂	—	32	2	no	—
21	C₃×C₁₆	D₃₂	1	1	yes	characteristic
22	Q₃₂	—	48	2	no	—
23	C₃₂	D₄₈	1	1	yes	characteristic
24	Dic₆	—	64	2	no	—
25	C₃×C₈	D₆₄	1	1	yes	characteristic
26	Q₁₆	—	96	2	no	—
27	C₁₆	D₉₆	1	1	yes	characteristic
28	C₃×C₄	D₁₂₈	1	1	yes	characteristic
29	Dic₃	—	128	2	no	—
30	Q₈	—	192	2	no	—
31	C₈	D₁₉₂	1	1	yes	characteristic
32	C₂×C₃	D₂₅₆	1	1	yes	characteristic
33	C₄	—	384	2	no	—
34	C₄	D₃₈₄	1	1	yes	characteristic
35	C₃	Q₁₀₂₄	1	1	yes	characteristic, complemented, Sylow
36	C₂	D₇₆₈	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
35. C₃	Q₁₀₂₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.