Subgroups — C₉×D₂₇ #92168

Order 486.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×D₂₇	C₃	1	1	yes	maximal, characteristic
3	C₉×D₉	—	3	1	no	maximal
4	C₃×C₂₇	—	2	1	no	—
5	C₃×C₂₇	C₂×C₃	1	1	yes	characteristic
6	C₉²	D₃	1	1	yes	characteristic
7	D₃×C₉	—	9	1	no	—
8	C₃×D₉	—	3	1	no	—
9	D₂₇	C₉	1	1	yes	characteristic, direct product factor
10	C₃×C₉	—	2	1	no	—
11	C₃×C₉	D₉	1	1	yes	characteristic
12	C₃×C₉	C₃×D₃	1	1	yes	characteristic
13	C₂₇	—	2	3	no	—
14	C₂₇	—	2	1	no	—
15	C₂₇	C₂×C₉	1	1	yes	characteristic, complemented
16	C₃×D₃	—	9	1	no	—
17	C₂×C₉	—	27	1	no	—
18	D₉	—	3	1	no	—
19	C₃²	C₃×D₉	1	1	yes	characteristic
20	C₉	—	2	3	no	—
21	C₉	—	2	1	no	—
22	C₉	—	2	1	no	—
23	C₉	D₂₇	1	1	yes	characteristic, direct product factor
24	C₉	D₃×C₉	1	1	yes	characteristic
25	C₂×C₃	—	27	1	no	—
26	D₃	—	9	1	no	—
27	C₃	—	2	1	no	—
28	C₃	C₉×D₉	1	1	yes	characteristic
29	C₃	C₃×D₂₇	1	1	yes	characteristic
30	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.