Subgroups — #6171

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, complemented
2	C₂×D₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#611	—	3	1	no	maximal
5	C₂×C₂₇	—	2	1	no	—
6	C₂×C₂₇	C₂²	1	1	yes	characteristic
7	D₂₇	—	2	1	no	—
8	C₂²×C₉	D₃	1	1	yes	characteristic
9	C₂×D₉	—	3	1	no	—
10	Dic₉	—	3	1	no	—
11	C₂₇	D₄	1	1	yes	characteristic, complemented, Sylow
12	#67	—	9	1	no	—
13	C₂×C₉	—	2	1	no	—
14	C₂×C₉	C₂×D₃	1	1	yes	characteristic
15	D₉	—	6	1	no	—
16	C₂²×C₃	D₉	1	1	yes	characteristic
17	C₂×D₃	—	9	1	no	—
18	Dic₃	—	9	1	no	—
19	C₉	#67	1	1	yes	characteristic
20	D₄	—	27	1	no	Sylow
21	C₂×C₃	—	2	1	no	—
22	C₂×C₃	C₂×D₉	1	1	yes	characteristic
23	D₃	—	18	1	no	—
24	C₂²	—	27	1	no	—
25	C₂²	D₂₇	1	1	yes	characteristic, complemented
26	C₄	—	27	1	no	—
27	C₃	#611	1	1	yes	characteristic
28	C₂	—	2	1	no	—
29	C₂	—	54	1	no	—
30	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.