Subgroups — C₂×Dic₂₇ #6170

Order 216.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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