Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20293425 | C2 | semidirect |
| 2. C2×#16812137 | C2 | semidirect |
| 3. C2×#16812134 | C2 | semidirect |
| 4. #20292897 | C2 | semidirect |
| 5. #20292890 | C2 | semidirect |
| 6. #20292676 | C2 | semidirect |
| 7. #20292609 | C2 | semidirect |
| 8. C2×#16812025 | C2 | semidirect |
| 9. #568×C107 | C2 | semidirect |
| 13. #16812139 | C22 | semidirect |
| 19. #16812134 | C22 | semidirect |
| 21. C2×#13133807 | C22 | semidirect |
| 23. C2×D856 | C22 | semidirect |
| 27. #16812045 | C22 | semidirect |
| 28. #16812027 | C22 | semidirect |
| 29. #16812025 | C22 | semidirect |
| 30. #16812025 | C22 | semidirect |
| 33. #131×C107 | C22 | semidirect |
| 148. C107 | #3068 | semidirect |
| 152. #568 | D107 | semidirect |
| 175. #131 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293425 | 2 |
| C2×#16812137 | 2 |
| C2×#16812134 | 2 |
| #20292897 | 2 |
| #20292890 | 2 |
| #20292676 | 2 |
| #20292609 | 2 |
| C2×#16812025 | 2 |
| #568×C107 | 2 |
| #3068 | 107 |