Subgroups — Dic₁₀₈ #88357

Order 432.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₄	C₂	1	2	yes	maximal
2	C₈×C₂₇	C₂	1	1	yes	maximal, characteristic
3	Dic₃₆	—	3	1	no	maximal
4	C₄×C₂₇	C₂²	1	1	yes	characteristic
5	Dic₂₇	—	2	2	no	—
6	Dic₁₈	—	3	2	no	—
7	C₈×C₉	D₃	1	1	yes	characteristic
8	C₂×C₂₇	D₄	1	1	yes	characteristic
9	Dic₁₂	—	9	1	no	—
10	C₄×C₉	C₂×D₃	1	1	yes	characteristic
11	Dic₉	—	6	2	no	—
12	C₂₇	Q₁₆	1	1	yes	characteristic, complemented, Sylow
13	Dic₆	—	9	2	no	—
14	C₃×C₈	D₉	1	1	yes	characteristic
15	C₂×C₉	D₁₂	1	1	yes	characteristic
16	Q₁₆	—	27	1	no	Sylow
17	C₃×C₄	C₂×D₉	1	1	yes	characteristic
18	Dic₃	—	18	2	no	—
19	C₉	Dic₁₂	1	1	yes	characteristic
20	Q₈	—	27	2	no	—
21	C₈	D₂₇	1	1	yes	characteristic
22	C₂×C₃	D₃₆	1	1	yes	characteristic
23	C₄	—	54	2	no	—
24	C₄	C₂×D₂₇	1	1	yes	characteristic
25	C₃	Dic₃₆	1	1	yes	characteristic
26	C₂	D₁₀₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₂₇	Q₁₆	semidirect

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