Subgroups — Dic₅₄ #6167

Order 216.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₇	C₂	1	2	yes	maximal
3	Dic₁₈	—	3	1	no	maximal
4	C₂×C₂₇	C₂²	1	1	yes	characteristic
5	C₄×C₉	D₃	1	1	yes	characteristic
6	Dic₉	—	3	2	no	—
7	C₂₇	Q₈	1	1	yes	characteristic, complemented, Sylow
8	Dic₆	—	9	1	no	—
9	C₂×C₉	C₂×D₃	1	1	yes	characteristic
10	C₃×C₄	D₉	1	1	yes	characteristic
11	Dic₃	—	9	2	no	—
12	C₉	Dic₆	1	1	yes	characteristic
13	Q₈	—	27	1	no	Sylow
14	C₂×C₃	C₂×D₉	1	1	yes	characteristic
15	C₄	—	27	2	no	—
16	C₄	D₂₇	1	1	yes	characteristic
17	C₃	Dic₁₈	1	1	yes	characteristic
18	C₂	C₂×D₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₂₇	Q₈	semidirect

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