Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16812134 | C2 | semidirect |
| 2. C2×#16812134 | C2 | semidirect |
| 3. #20293394 | C2 | semidirect |
| 4. #20292895 | C2 | semidirect |
| 5. #20292892 | C2 | semidirect |
| 6. #20292675 | C2 | semidirect |
| 7. #20292611 | C2 | semidirect |
| 8. C2×#16812025 | C2 | semidirect |
| 9. #575×C107 | C2 | semidirect |
| 16. C2×#13133805 | C22 | semidirect |
| 18. C2×#13133803 | C22 | semidirect |
| 20. #16812116 | C22 | semidirect |
| 25. #16812044 | C22 | semidirect |
| 26. #16812028 | C22 | semidirect |
| 27. #16812026 | C22 | semidirect |
| 28. #16812025 | C22 | semidirect |
| 32. #137×C107 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C107 | C22 | semidirect |
| 148. C107 | #3068 | semidirect |
| 149. #575 | D107 | semidirect |
| 162. #137 | C2×D107 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| #20293394 | 2 |
| #20292895 | 2 |
| #20292892 | 2 |
| #20292675 | 2 |
| #20292611 | 2 |
| C2×#16812025 | 2 |
| #575×C107 | 2 |
| #3068 | 107 |