Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20293258 | C2 | semidirect |
| 3. #20292990 | C2 | semidirect |
| 4. #20292988 | C2 | semidirect |
| 5. #20292983 | C2 | semidirect |
| 6. #20292972 | C2 | semidirect |
| 7. #20292633 | C2 | semidirect |
| 8. #20292623 | C2 | semidirect |
| 9. C2×#16812029 | C2 | semidirect |
| 10. #20292585 | C2 | semidirect |
| 11. #417×C107 | C2 | semidirect |
| 15. #16812108 | C22 | semidirect |
| 18. #16812100 | C22 | semidirect |
| 26. #16812033 | C22 | semidirect |
| 27. #16812033 | C22 | semidirect |
| 30. #16812030 | C22 | semidirect |
| 31. #16812030 | C22 | semidirect |
| 34. #16812019 | C22 | semidirect |
| 35. C8×Dic107 | C22 | semidirect |
| 39. #103×C107 | C22 | semidirect |
| 40. #102×C107 | C22 | semidirect |
| 136. C107 | #3136 | semidirect |
| 144. #417 | D107 | semidirect |
| 167. #103 | C2×D107 | semidirect |
| 174. #102 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293258 | 2 |
| #20293191 | 2 |
| #20292990 | 2 |
| #20292988 | 2 |
| #20292983 | 2 |
| #20292972 | 2 |
| #20292633 | 2 |
| #20292623 | 2 |
| C2×#16812029 | 2 |
| #20292585 | 2 |
| #417×C107 | 2 |
| #3136 | 107 |