Subgroups — C₂₇⋊C₈ #6164

Order 216.

16 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	C₉⋊C₈	—	3	1	no	maximal
3	C₂×C₂₇	C₄	1	1	yes	characteristic
4	C₄×C₉	D₃	1	1	yes	characteristic
5	C₂₇	C₈	1	1	yes	characteristic, complemented, Sylow
6	C₃⋊C₈	—	9	1	no	—
7	C₂×C₉	Dic₃	1	1	yes	characteristic
8	C₃×C₄	D₉	1	1	yes	characteristic
9	C₉	C₃⋊C₈	1	1	yes	characteristic
10	C₈	—	27	1	no	Sylow
11	C₂×C₃	Dic₉	1	1	yes	characteristic
12	C₄	D₂₇	1	1	yes	characteristic
13	C₃	C₉⋊C₈	1	1	yes	characteristic
14	C₂	Dic₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₂₇	C₈	semidirect

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

subgroup	index
C₄×C₂₇	2
C₉⋊C₈	3