Subgroups — #66419

Order 324.

31 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4208	C₂	1	1	yes	maximal, characteristic
2	#1088	C₃	1	1	yes	maximal, characteristic
3	#737	C₄	1	1	yes	characteristic, complemented, Sylow
4	#272	C₂×C₃	1	1	yes	characteristic
5	D₃×C₉	—	6	2	no	—
6	C₄×C₉	—	9	1	no	maximal
7	3₋¹⁺²	—	4	2	no	—
8	H(3,𝔽₃)	C₃×C₄	1	1	yes	characteristic
9	C₃×C₉	—	2	2	no	—
10	C₃×D₃	—	6	2	no	—
11	C₂×C₉	—	9	1	no	—
12	C₃×C₄	—	9	1	no	—
13	C₃²	—	2	2	no	—
14	C₉	—	4	2	no	—
15	C₉	#157	1	1	yes	characteristic
16	C₂×C₃	—	9	1	no	—
17	D₃	—	6	2	no	—
18	C₄	—	9	1	no	Sylow
19	C₃	—	6	2	no	—
20	C₃	C₃×#157	1	1	yes	characteristic
21	C₂	—	9	1	no	—

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

N	H ≅ G/N	type
3. #737	C₄	semidirect

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