Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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. #10597790 | C2 | semidirect |
| 2. C2×C13×D12 | C2 | semidirect |
| 3. C3×#6099 | C2 | semidirect |
| 4. #10597602 | C2 | semidirect |
| 5. #10597597 | C2 | semidirect |
| 10. D156 | C22 | semidirect |
| 12. Dic78 | C22 | semidirect |
| 15. C3×#1055 | C22 | semidirect |
| 20. #6099 | D3 | semidirect |
| 36. #1055 | C2×D3 | semidirect |
| 50. C2×D12 | D13 | semidirect |
| 54. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 74. C13 | #908 | semidirect |
| 102. C3 | #88186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597790 | 2 |
| C2×C13×D12 | 2 |
| C3×#6099 | 2 |
| #10597602 | 2 |
| #10597597 | 2 |
| #88186 | 3 |
| #908 | 13 |