Subgroups — Dic₁₅₃₆ #72212034

Order 6144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₆₈	C₂	1	2	yes	maximal
2	Dic₃₈₄	—	2	2	no	—
3	Q₂₀₄₈	—	3	1	no	maximal, Sylow
4	Q₁₀₂₄	—	3	2	no	—
5	C₃×C₁₀₂₄	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅₁₂	C₂²	1	1	yes	characteristic
7	C₁₀₂₄	D₃	1	1	yes	characteristic
8	Dic₁₉₂	—	4	2	no	—
9	C₃×C₂₅₆	D₄	1	1	yes	characteristic
10	Q₅₁₂	—	6	2	no	—
11	C₅₁₂	C₂×D₃	1	1	yes	characteristic
12	Dic₉₆	—	8	2	no	—
13	C₃×C₁₂₈	D₈	1	1	yes	characteristic
14	Q₂₅₆	—	12	2	no	—
15	C₂₅₆	D₁₂	1	1	yes	characteristic
16	Dic₄₈	—	16	2	no	—
17	C₃×C₆₄	D₁₆	1	1	yes	characteristic
18	Q₁₂₈	—	24	2	no	—
19	C₁₂₈	D₂₄	1	1	yes	characteristic
20	Dic₂₄	—	32	2	no	—
21	C₃×C₃₂	D₃₂	1	1	yes	characteristic
22	Q₆₄	—	48	2	no	—
23	C₆₄	D₄₈	1	1	yes	characteristic
24	Dic₁₂	—	64	2	no	—
25	C₃×C₁₆	D₆₄	1	1	yes	characteristic
26	Q₃₂	—	96	2	no	—
27	C₃₂	D₉₆	1	1	yes	characteristic
28	Dic₆	—	128	2	no	—
29	C₃×C₈	D₁₂₈	1	1	yes	characteristic
30	Q₁₆	—	192	2	no	—
31	C₁₆	D₁₉₂	1	1	yes	characteristic
32	C₃×C₄	D₂₅₆	1	1	yes	characteristic
33	Dic₃	—	256	2	no	—
34	Q₈	—	384	2	no	—
35	C₈	D₃₈₄	1	1	yes	characteristic
36	C₂×C₃	D₅₁₂	1	1	yes	characteristic
37	C₄	—	768	2	no	—
38	C₄	D₇₆₈	1	1	yes	characteristic
39	C₃	Q₂₀₄₈	1	1	yes	characteristic, complemented, Sylow
40	C₂	D₁₅₃₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
39. C₃	Q₂₀₄₈	semidirect

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