Subgroups — #733⋊C₄ #66333

Order 324.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#733	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²⋊C₄	—	3	3	no	maximal
3	C₃×Dic₉	—	3	1	no	maximal
4	#733	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×3₋¹⁺²	D₃	1	3	yes	—
6	C₂×C₃×C₉	D₃	1	1	yes	characteristic
7	C₃×Dic₃	—	9	1	no	—
8	Dic₉	—	3	1	no	—
9	Dic₉	—	3	3	no	—
10	3₋¹⁺²	Dic₃	1	3	yes	—
11	C₃×C₉	Dic₃	1	1	yes	characteristic
12	C₂×C₃²	C₃⋊D₃	1	1	yes	characteristic
13	C₂×C₉	—	3	1	no	—
14	C₂×C₉	—	3	3	no	—
15	C₃×C₄	—	27	1	no	—
16	Dic₃	—	9	1	no	—
17	C₃²	C₃⋊Dic₃	1	1	yes	characteristic
18	C₉	—	3	1	no	—
19	C₉	—	3	3	no	—
20	C₂×C₃	—	3	1	no	—
21	C₂×C₃	#272	1	1	yes	characteristic
22	C₄	—	27	1	no	Sylow
23	C₃	—	3	1	no	—
24	C₃	#1084	1	1	yes	characteristic
25	C₂	#733⋊C₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
4. #733	C₄	semidirect

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