Subgroups — C₉×C₃⋊D₃ #4203

Order 162.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic
3	D₃×C₉	—	3	4	no	maximal
4	C₃³	C₂×C₃	1	1	yes	characteristic
5	C₃×C₉	—	2	4	no	—
6	C₃×C₉	D₃	1	4	yes	complemented
7	C₃⋊D₃	C₉	1	1	yes	characteristic, direct product factor
8	C₃×D₃	—	3	4	no	—
9	C₂×C₉	—	9	1	no	—
10	C₃²	—	2	4	no	—
11	C₃²	C₂×C₉	1	1	yes	characteristic, complemented
12	C₃²	C₃×D₃	1	4	yes	—
13	C₉	—	2	4	no	—
14	C₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃	—	9	1	no	—
16	D₃	—	3	4	no	—
17	C₃	—	2	4	no	—
18	C₃	D₃×C₉	1	4	yes	complemented
19	C₃	C₃×C₃⋊D₃	1	1	yes	characteristic
20	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.