Subgroups — #66328

Order 324.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊Dic₃	—	3	1	no	maximal
3	C₃×Dic₉	—	3	3	no	maximal
4	C₃²⋊C₉	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃³	D₃	1	1	yes	characteristic
6	C₂×C₃×C₉	D₃	1	3	yes	—
7	C₃⋊Dic₃	—	3	1	no	—
8	C₃×Dic₃	—	9	3	no	—
9	C₃×Dic₃	—	9	1	no	—
10	Dic₉	—	3	3	no	—
11	C₃³	Dic₃	1	1	yes	characteristic
12	C₃×C₉	Dic₃	1	3	yes	complemented
13	C₂×C₃²	—	3	1	no	—
14	C₂×C₃²	—	6	1	no	—
15	C₂×C₃²	D₉	1	3	yes	—
16	C₂×C₃²	C₃⋊D₃	1	1	yes	characteristic
17	C₂×C₉	—	3	3	no	—
18	C₃×C₄	—	27	1	no	—
19	Dic₃	—	9	3	no	—
20	Dic₃	—	9	1	no	—
21	C₃²	—	3	1	no	—
22	C₃²	—	6	1	no	—
23	C₃²	Dic₉	1	3	yes	complemented
24	C₃²	C₃⋊Dic₃	1	1	yes	characteristic
25	C₉	—	3	3	no	—
26	C₂×C₃	—	2	1	no	—
27	C₂×C₃	—	3	3	no	—
28	C₂×C₃	C₃⋊D₉	1	1	yes	characteristic
29	C₂×C₃	#272	1	1	yes	characteristic
30	C₄	—	27	1	no	Sylow
31	C₃	—	2	1	no	—
32	C₃	—	3	3	no	—
33	C₃	C₃⋊Dic₉	1	1	yes	characteristic
34	C₃	#1084	1	1	yes	characteristic
35	C₂	#4181	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.