Subgroups — D₃×3₋¹⁺² #4201

Order 162.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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