Subgroups — D₂₇₆ #10587787

Order 552.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₉₂	—	3	1	no	maximal, Hall
4	C₂×C₃×C₂₃	C₂²	1	1	yes	characteristic
5	D₆₉	—	2	2	no	—
6	C₂×D₂₃	—	3	2	no	—
7	C₄×C₂₃	D₃	1	1	yes	characteristic, complemented
8	C₃×C₂₃	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₂₃	C₂×D₃	1	1	yes	characteristic
10	D₂₃	—	6	2	no	—
11	D₁₂	—	23	1	no	maximal, Hall
12	C₂₃	D₁₂	1	1	yes	characteristic, complemented, Sylow
13	C₂×D₃	—	23	2	no	—
14	C₃×C₄	D₂₃	1	1	yes	characteristic, complemented
15	D₄	—	69	1	no	Sylow
16	C₂×C₃	C₂×D₂₃	1	1	yes	characteristic
17	D₃	—	46	2	no	—
18	C₂²	—	69	2	no	—
19	C₄	D₆₉	1	1	yes	characteristic, complemented
20	C₃	D₉₂	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	138	2	no	—
22	C₂	C₂×D₆₉	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.