Finite Group DatabasebetaFinite Group DatabasebetaOrder 5184.
1066 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #72213723 | C2 | direct (N × H) |
| 7. C2×#10620193 | C4 | semidirect |
| 9. C2×#10620192 | C4 | semidirect |
| 15. C2×#66472 | C8 | semidirect |
| 21. #10620193 | C2×C4 | semidirect |
| 22. #10620192 | C2×C4 | semidirect |
| 23. C2×C32×C3⋊Dic3 | C8 | semidirect |
| 24. #10620150 | C8 | semidirect |
| 34. #66472 | C2×C8 | semidirect |
| 37. C32×C3⋊Dic3 | C2×C8 | semidirect |
| 49. C2×C34 | C4×C8 | semidirect |
| 51. C3⋊(C3⋊(C3⋊D3)) | C4×C8 | semidirect |
| 80. C34 | C2×C4×C8 | semidirect |
| 103. C2×C3⋊Dic3 | AGL(1,𝔽9) | semidirect |
| 160. C3⋊Dic3 | C2×AGL(1,𝔽9) | semidirect |
| 184. C2×C32 | C4×AGL(1,𝔽9) | semidirect |
| 230. C32 | C2×C4×AGL(1,𝔽9) | semidirect |
| 268. C2 | #72213723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10620193 | 2 |
| C2×#13049409 | 2 |
| #72213723 | 2 |
| C22×#10620192 | 2 |
| C2×C4×AGL(1,𝔽9) | 9 |