Subgroups — #66326

Order 324.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#732	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₃⋊Dic₃)⋊C₃	—	3	1	no	maximal
4	#732	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×H(3,𝔽₃)	—	2	1	no	—
6	C₂×H(3,𝔽₃)	D₃	1	1	yes	characteristic
7	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
8	C₃⋊Dic₃	—	3	1	no	—
9	C₃×Dic₃	—	9	1	no	—
10	Dic₉	—	9	1	no	—
11	H(3,𝔽₃)	—	2	1	no	—
12	H(3,𝔽₃)	Dic₃	1	1	yes	characteristic
13	C₃×C₉	C₃×C₄	1	1	yes	characteristic, complemented
14	C₂×C₃²	—	3	1	no	—
15	C₂×C₃²	—	6	1	no	—
16	C₂×C₃²	C₃×D₃	1	1	yes	characteristic
17	C₂×C₉	—	3	1	no	—
18	C₃×C₄	—	27	1	no	—
19	Dic₃	—	9	1	no	—
20	Dic₃	—	27	1	no	—
21	C₃²	—	3	1	no	—
22	C₃²	—	6	1	no	—
23	C₃²	C₃×Dic₃	1	1	yes	characteristic
24	C₉	—	3	1	no	—
25	C₂×C₃	—	3	1	no	—
26	C₂×C₃	—	9	1	no	—
27	C₂×C₃	—	18	1	no	—
28	C₂×C₃	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
29	C₄	—	27	1	no	Sylow
30	C₃	—	3	1	no	—
31	C₃	—	9	1	no	—
32	C₃	—	18	1	no	—
33	C₃	(C₃⋊Dic₃)⋊C₃	1	1	yes	characteristic
34	C₂	#4179	1	1	yes	characteristic

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.