Subgroups — Dic₁₄₇₂ #19212124

Order 5888.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₃₆	C₂	1	2	yes	maximal
2	C₂₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	Dic₃₆₈	—	2	2	no	—
4	C₂₃×C₆₄	C₂²	1	1	yes	characteristic
5	Dic₁₈₄	—	4	2	no	—
6	C₂₃×C₃₂	D₄	1	1	yes	characteristic
7	Dic₉₂	—	8	2	no	—
8	C₁₆×C₂₃	D₈	1	1	yes	characteristic
9	Q₂₅₆	—	23	1	no	maximal, Sylow
10	Dic₄₆	—	16	2	no	—
11	C₈×C₂₃	D₁₆	1	1	yes	characteristic
12	Q₁₂₈	—	23	2	no	—
13	C₁₂₈	D₂₃	1	1	yes	characteristic
14	C₄×C₂₃	D₃₂	1	1	yes	characteristic
15	Dic₂₃	—	32	2	no	—
16	Q₆₄	—	46	2	no	—
17	C₆₄	C₂×D₂₃	1	1	yes	characteristic
18	C₂×C₂₃	D₆₄	1	1	yes	characteristic
19	Q₃₂	—	92	2	no	—
20	C₃₂	D₉₂	1	1	yes	characteristic
21	C₂₃	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
22	Q₁₆	—	184	2	no	—
23	C₁₆	D₁₈₄	1	1	yes	characteristic
24	Q₈	—	368	2	no	—
25	C₈	D₃₆₈	1	1	yes	characteristic
26	C₄	—	736	2	no	—
27	C₄	D₇₃₆	1	1	yes	characteristic
28	C₂	D₁₄₇₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
21. C₂₃	Q₂₅₆	semidirect