Subgroups — Dic₁₂₆ #92608

Order 504.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic
2	Dic₆₃	C₂	1	2	yes	maximal
3	Dic₄₂	—	3	1	no	maximal
4	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₇	D₃	1	1	yes	characteristic
6	Dic₂₁	—	3	2	no	—
7	Dic₁₈	—	7	1	no	maximal, Hall
8	C₇×C₉	Q₈	1	1	yes	characteristic, complemented, Hall
9	Dic₁₄	—	9	1	no	Hall
10	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
11	C₄×C₉	D₇	1	1	yes	characteristic
12	Dic₉	—	7	2	no	—
13	C₄×C₇	D₉	1	1	yes	characteristic
14	Dic₇	—	9	2	no	—
15	Dic₆	—	21	1	no	—
16	C₃×C₇	Dic₆	1	1	yes	characteristic
17	C₂×C₉	C₂×D₇	1	1	yes	characteristic
18	C₂×C₇	C₂×D₉	1	1	yes	characteristic
19	C₃×C₄	D₂₁	1	1	yes	characteristic
20	Dic₃	—	21	2	no	—
21	C₉	Dic₁₄	1	1	yes	characteristic, complemented, Sylow
22	Q₈	—	63	1	no	Sylow
23	C₇	Dic₁₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	C₂×D₂₁	1	1	yes	characteristic
25	C₄	—	63	2	no	—
26	C₄	D₆₃	1	1	yes	characteristic
27	C₃	Dic₄₂	1	1	yes	characteristic
28	C₂	C₂×D₆₃	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.