Subgroups — D₃×H(3,𝔽₃) #4199

Order 162.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²×D₃	C₃	1	4	yes	maximal, complemented
3	C₂×H(3,𝔽₃)	—	3	1	no	maximal
4	C₃³	C₂×C₃	1	4	yes	complemented
5	H(3,𝔽₃)	—	2	4	no	—
6	H(3,𝔽₃)	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₃²	—	3	4	no	—
8	C₃×D₃	—	3	4	no	—
9	C₃×D₃	C₃²	1	1	yes	characteristic
10	C₃²	—	2	4	no	—
11	C₃²	—	3	4	no	—
12	C₃²	—	6	4	no	—
13	C₃²	C₃×D₃	1	4	yes	complemented
14	C₃²	C₂×C₃²	1	1	yes	characteristic
15	C₂×C₃	—	3	1	no	—
16	C₂×C₃	—	9	4	no	—
17	D₃	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
18	C₃	—	2	1	no	—
19	C₃	—	3	4	no	—
20	C₃	—	6	4	no	—
21	C₃	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
22	C₃	C₃²×D₃	1	1	yes	characteristic
23	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.