Subgroups — C₉×D₉ #4167

Order 162.

25 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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