Subgroups — Dic₇₆ #64518

Order 304.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₈	C₂	1	2	yes	maximal
2	C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉	C₂²	1	1	yes	characteristic
4	Dic₁₉	—	2	2	no	—
5	C₂×C₁₉	D₄	1	1	yes	characteristic
6	C₁₉	Q₁₆	1	1	yes	characteristic, complemented, Sylow
7	Q₁₆	—	19	1	no	maximal, Sylow
8	Q₈	—	19	2	no	—
9	C₈	D₁₉	1	1	yes	characteristic
10	C₄	—	38	2	no	—
11	C₄	C₂×D₁₉	1	1	yes	characteristic
12	C₂	D₇₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₁₉	Q₁₆	semidirect

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