Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. C13×#235 | C2 | semidirect |
| 2. C2×C13×D12 | C2 | semidirect |
| 3. C3×C13×M16 | C2 | semidirect |
| 4. C13×D24 | C2 | semidirect |
| 5. C13×#204 | C2 | semidirect |
| 12. C13×D12 | C22 | semidirect |
| 14. C13×Dic6 | C22 | semidirect |
| 15. C3×C8×C13 | C22 | semidirect |
| 20. C13×M16 | D3 | semidirect |
| 36. C8×C13 | C2×D3 | semidirect |
| 37. #908 | C13 | direct (N × H) |
| 49. #235 | C2×C13 | semidirect |
| 50. C2×D12 | C2×C13 | semidirect |
| 51. C3×M16 | C2×C13 | semidirect |
| 52. D24 | C2×C13 | semidirect |
| 53. #204 | C2×C13 | semidirect |
| 54. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 65. D12 | C22×C13 | semidirect |
| 67. Dic6 | C22×C13 | semidirect |
| 68. C3×C8 | C22×C13 | semidirect |
| 73. M16 | D3×C13 | semidirect |
| 74. C13 | #908 | direct (N × H) |
| 90. C8 | C2×D3×C13 | semidirect |
| 102. C3 | C13×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#235 | 2 |
| C2×C13×D12 | 2 |
| C3×C13×M16 | 2 |
| C13×D24 | 2 |
| C13×#204 | 2 |
| C13×AGL(1,ℤ/8) | 3 |
| #908 | 13 |