Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 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. C2×#64625 | C2 | semidirect |
| 2. C2×C13×#67 | C2 | semidirect |
| 3. C22×C3×Dic13 | C2 | semidirect |
| 4. C2×#64605 | C2 | semidirect |
| 5. C2×#64604 | C2 | semidirect |
| 6. C2×#64601 | C2 | semidirect |
| 7. #10597748 | C2 | direct (N × H) |
| 8. C2×D3×Dic13 | C2 | semidirect |
| 13. #64625 | C22 | semidirect |
| 15. C13×#67 | C22 | semidirect |
| 19. C2×C3×Dic13 | C22 | semidirect |
| 20. #64605 | C22 | semidirect |
| 21. #64604 | C22 | semidirect |
| 22. #64601 | C22 | semidirect |
| 23. D3×Dic13 | C22 | semidirect |
| 28. C22×Dic13 | D3 | semidirect |
| 54. C2×Dic13 | C2×D3 | semidirect |
| 59. C2×C3×C13 | #41 | semidirect |
| 76. C2×#67 | D13 | semidirect |
| 82. C3×C13 | C2×#41 | semidirect |
| 86. C2×C13 | #235 | semidirect |
| 96. #67 | C2×D13 | semidirect |
| 111. C13 | C2×#235 | semidirect |
| 138. C2×C3 | #6129 | semidirect |
| 153. C3 | C2×#6129 | semidirect |
| 157. C2 | #10597748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64625 | 2 |
| C2×C13×#67 | 2 |
| C22×C3×Dic13 | 2 |
| C2×#64605 | 2 |
| C2×#64604 | 2 |
| C2×#64601 | 2 |
| #10597748 | 2 |
| C2×D3×Dic13 | 2 |
| C2×#6129 | 3 |
| C2×#235 | 13 |