Subgroups — AGL(1,ℤ/27) #92186

Order 486.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6875	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	D₉⋊C₉	—	3	1	no	maximal
4	C₂₇⋊C₃	—	2	1	no	—
5	C₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₉⋊C₉	D₃	1	1	yes	characteristic
7	D₃×C₉	—	9	1	no	—
8	C₃×D₉	—	3	1	no	—
9	D₂₇	C₉	1	1	yes	characteristic, complemented
10	C₃×C₉	—	3	1	no	—
11	C₃×C₉	C₃×D₃	1	1	yes	characteristic
12	C₂₇	—	2	1	no	—
13	C₂₇	—	6	1	no	—
14	C₂₇	C₂×C₉	1	1	yes	characteristic, complemented
15	C₃×D₃	—	9	1	no	—
16	C₂×C₉	—	27	1	no	—
17	D₉	—	3	1	no	—
18	C₃²	AGL(1,ℤ/9)	1	1	yes	characteristic
19	C₉	—	2	1	no	—
20	C₉	—	9	1	no	—
21	C₉	D₃×C₉	1	1	yes	characteristic
22	C₂×C₃	—	27	1	no	—
23	D₃	—	9	1	no	—
24	C₃	—	3	1	no	—
25	C₃	D₉⋊C₉	1	1	yes	characteristic
26	C₂	—	27	1	no	Sylow

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.