Subgroups — C₂×C₃²⋊C₉ #4188

Order 162.

46 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, direct product factor, Sylow
2	C₂×C₃³	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃×C₉	C₃	1	3	yes	maximal, complemented
4	C₃³	C₂×C₃	1	1	yes	characteristic
5	C₃×C₉	C₂×C₃	1	3	yes	complemented
6	C₂×C₃²	—	3	1	no	—
7	C₂×C₃²	—	3	2	no	—
8	C₂×C₃²	C₉	1	3	yes	complemented
9	C₂×C₃²	C₃²	1	1	yes	characteristic
10	C₂×C₉	—	3	3	no	—
11	C₃²	—	3	1	no	—
12	C₃²	—	3	2	no	—
13	C₃²	C₂×C₉	1	3	yes	complemented
14	C₃²	C₂×C₃²	1	1	yes	characteristic
15	C₉	—	3	3	no	—
16	C₂×C₃	—	3	3	no	—
17	C₂×C₃	C₃×C₉	1	1	yes	characteristic
18	C₂×C₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₂×C₃	3₋¹⁺²	1	2	yes	—
20	C₃	—	3	3	no	—
21	C₃	C₂×C₃×C₉	1	1	yes	characteristic
22	C₃	C₂×H(3,𝔽₃)	1	1	yes	characteristic
23	C₃	C₂×3₋¹⁺²	1	2	yes	—
24	C₂	C₃²⋊C₉	1	1	yes	characteristic, direct product factor, 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.