Subgroups — C₈×#733 #10619521

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	C₈×3₋¹⁺²	C₃	1	3	yes	maximal
3	C₃×C₈×C₉	C₃	1	1	yes	maximal, characteristic
4	C₂×#733	C₄	1	1	yes	characteristic
5	C₄×3₋¹⁺²	C₂×C₃	1	3	yes	—
6	C₃×C₄×C₉	C₂×C₃	1	1	yes	characteristic
7	#733	C₈	1	1	yes	characteristic, direct product factor, Sylow
8	C₃²×C₈	C₃²	1	1	yes	characteristic
9	C₈×C₉	—	3	1	no	—
10	C₈×C₉	—	3	3	no	—
11	C₂×3₋¹⁺²	C₃×C₄	1	3	yes	—
12	C₂×C₃×C₉	C₃×C₄	1	1	yes	characteristic
13	C₃²×C₄	C₂×C₃²	1	1	yes	characteristic
14	C₄×C₉	—	3	1	no	—
15	C₄×C₉	—	3	3	no	—
16	3₋¹⁺²	C₃×C₈	1	3	yes	—
17	C₃×C₉	C₃×C₈	1	1	yes	characteristic
18	C₃×C₈	—	3	1	no	—
19	C₃×C₈	H(3,𝔽₃)	1	1	yes	characteristic
20	C₂×C₃²	C₃²×C₄	1	1	yes	characteristic
21	C₂×C₉	—	3	1	no	—
22	C₂×C₉	—	3	3	no	—
23	C₃×C₄	—	3	1	no	—
24	C₃×C₄	C₂×H(3,𝔽₃)	1	1	yes	characteristic
25	C₃²	C₃²×C₈	1	1	yes	characteristic
26	C₉	—	3	1	no	—
27	C₉	—	3	3	no	—
28	C₈	#733	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	C₄×H(3,𝔽₃)	1	1	yes	characteristic
31	C₄	C₂×#733	1	1	yes	characteristic
32	C₃	—	3	1	no	—
33	C₃	C₈×H(3,𝔽₃)	1	1	yes	characteristic
34	C₂	C₄×#733	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #733	C₈	direct (N × H)
28. C₈	#733	direct (N × H)

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