Subgroups — #66410

Order 324.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#737	C₂	1	1	yes	maximal, characteristic
2	#1084	C₃	1	1	yes	maximal, characteristic
3	C₉×Dic₃	—	3	4	no	maximal
4	#737	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×3₋¹⁺²	—	2	4	no	—
6	C₂×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₉	D₃	1	4	yes	—
8	C₃×Dic₃	—	3	4	no	—
9	C₄×C₉	—	9	1	no	—
10	3₋¹⁺²	—	2	4	no	—
11	H(3,𝔽₃)	C₃×C₄	1	1	yes	characteristic
12	C₃×C₉	Dic₃	1	4	yes	complemented
13	C₂×C₃²	C₃×D₃	1	4	yes	—
14	C₂×C₉	—	2	4	no	—
15	C₂×C₉	C₃⋊D₃	1	1	yes	characteristic
16	C₃×C₄	—	9	1	no	—
17	Dic₃	—	3	4	no	—
18	C₃²	C₃×Dic₃	1	4	yes	—
19	C₉	—	2	4	no	—
20	C₉	C₃⋊Dic₃	1	1	yes	characteristic
21	C₂×C₃	—	3	4	no	—
22	C₂×C₃	C₃×C₃⋊D₃	1	1	yes	characteristic
23	C₄	—	9	1	no	Sylow
24	C₃	—	3	4	no	—
25	C₃	C₃×C₃⋊Dic₃	1	1	yes	characteristic
26	C₂	#4208	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #737	C₄	semidirect
12. C₃×C₉	Dic₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.