Subgroups — Dic₃₇₇₆ #28476607

Order 15104.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₈₈₈	C₂	1	2	yes	maximal
2	C₅₉×C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	Dic₉₄₄	—	2	2	no	—
4	C₅₉×C₆₄	C₂²	1	1	yes	characteristic
5	Dic₄₇₂	—	4	2	no	—
6	C₃₂×C₅₉	D₄	1	1	yes	characteristic
7	Dic₂₃₆	—	8	2	no	—
8	C₁₆×C₅₉	D₈	1	1	yes	characteristic
9	Dic₁₁₈	—	16	2	no	—
10	C₈×C₅₉	D₁₆	1	1	yes	characteristic
11	Q₂₅₆	—	59	1	no	maximal, Sylow
12	C₄×C₅₉	D₃₂	1	1	yes	characteristic
13	Dic₅₉	—	32	2	no	—
14	Q₁₂₈	—	59	2	no	—
15	C₁₂₈	D₅₉	1	1	yes	characteristic
16	C₂×C₅₉	D₆₄	1	1	yes	characteristic
17	Q₆₄	—	118	2	no	—
18	C₆₄	C₂×D₅₉	1	1	yes	characteristic
19	C₅₉	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
20	Q₃₂	—	236	2	no	—
21	C₃₂	D₂₃₆	1	1	yes	characteristic
22	Q₁₆	—	472	2	no	—
23	C₁₆	D₄₇₂	1	1	yes	characteristic
24	Q₈	—	944	2	no	—
25	C₈	D₉₄₄	1	1	yes	characteristic
26	C₄	—	1888	2	no	—
27	C₄	D₁₈₈₈	1	1	yes	characteristic
28	C₂	D₃₇₇₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₅₉	Q₂₅₆	semidirect

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