Subgroups — C₄×D₂₇ #6168

Order 216.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₉	—	3	1	no	maximal
5	C₂×C₂₇	C₂²	1	1	yes	characteristic
6	D₂₇	C₄	1	2	yes	direct product factor
7	C₂×D₉	—	3	1	no	—
8	C₄×C₉	D₃	1	1	yes	characteristic
9	Dic₉	—	3	1	no	—
10	C₂₇	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₄×D₃	—	9	1	no	—
12	C₂×C₉	C₂×D₃	1	1	yes	characteristic
13	D₉	—	3	2	no	—
14	C₂×D₃	—	9	1	no	—
15	C₃×C₄	D₉	1	1	yes	characteristic
16	Dic₃	—	9	1	no	—
17	C₉	C₄×D₃	1	1	yes	characteristic
18	C₂×C₄	—	27	1	no	Sylow
19	C₂×C₃	C₂×D₉	1	1	yes	characteristic
20	D₃	—	9	2	no	—
21	C₂²	—	27	1	no	—
22	C₄	—	27	1	no	—
23	C₄	D₂₇	1	1	yes	characteristic, direct product factor
24	C₃	C₄×D₉	1	1	yes	characteristic
25	C₂	—	27	2	no	—
26	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.