Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #20293182 | C2 | semidirect |
| 3. #20292990 | C2 | semidirect |
| 4. #20292975 | C2 | semidirect |
| 5. #20292974 | C2 | semidirect |
| 6. #20292973 | C2 | semidirect |
| 7. #20292630 | C2 | semidirect |
| 8. C4×#13133801 | C2 | semidirect |
| 9. #486×C107 | C2 | semidirect |
| 14. #16812109 | C22 | semidirect |
| 19. #16812100 | C22 | semidirect |
| 26. #16812031 | C22 | semidirect |
| 27. #16812030 | C22 | semidirect |
| 28. #16812029 | C22 | semidirect |
| 29. #16812019 | C22 | semidirect |
| 30. C4×C107⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C107 | C22 | semidirect |
| 33. #102×C107 | C22 | semidirect |
| 34. C4×C8×C107 | C22 | semidirect |
| 124. C107 | #3138 | semidirect |
| 131. #486 | D107 | semidirect |
| 139. C4⋊Q8 | C2×D107 | semidirect |
| 155. #102 | C2×D107 | semidirect |
| 158. C4×C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293182 | 2 |
| #127×D107 | 2 |
| #20292990 | 2 |
| #20292975 | 2 |
| #20292974 | 2 |
| #20292973 | 2 |
| #20292630 | 2 |
| C4×#13133801 | 2 |
| #486×C107 | 2 |
| #3138 | 107 |