Subgroups — #733⋊C₈ #10619512

Order 648.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#733	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²⋊C₈	—	3	3	no	maximal
3	C₃×C₉⋊C₈	—	3	1	no	maximal
4	C₂×#733	C₄	1	1	yes	characteristic
5	C₄×3₋¹⁺²	D₃	1	3	yes	—
6	C₃×C₄×C₉	D₃	1	1	yes	characteristic
7	#733	C₈	1	1	yes	characteristic, complemented, Sylow
8	C₃×C₃⋊C₈	—	9	1	no	—
9	C₉⋊C₈	—	3	1	no	—
10	C₉⋊C₈	—	3	3	no	—
11	C₂×3₋¹⁺²	Dic₃	1	3	yes	—
12	C₂×C₃×C₉	Dic₃	1	1	yes	characteristic
13	C₃²×C₄	C₃⋊D₃	1	1	yes	characteristic
14	C₄×C₉	—	6	1	no	—
15	C₄×C₉	—	6	3	no	—
16	3₋¹⁺²	C₃⋊C₈	1	3	yes	—
17	C₃×C₉	C₃⋊C₈	1	1	yes	characteristic
18	C₃×C₈	—	27	1	no	—
19	C₃⋊C₈	—	9	1	no	—
20	C₂×C₃²	C₃⋊Dic₃	1	1	yes	characteristic
21	C₂×C₉	—	6	1	no	—
22	C₂×C₉	—	6	3	no	—
23	C₃×C₄	—	6	1	no	—
24	C₃×C₄	#272	1	1	yes	characteristic
25	C₃²	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
26	C₉	—	6	1	no	—
27	C₉	—	6	3	no	—
28	C₈	—	27	1	no	Sylow
29	C₂×C₃	—	6	1	no	—
30	C₂×C₃	#1084	1	1	yes	characteristic
31	C₄	#733⋊C₂	1	1	yes	characteristic
32	C₃	—	6	1	no	—
33	C₃	#6180	1	1	yes	characteristic
34	C₂	#733⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #733	C₈	semidirect

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