Subgroups — D₇₆ #3888

Order 152.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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