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. #20293425 | C2 | semidirect |
| 2. C2×#16812135 | C2 | semidirect |
| 3. #20293394 | C2 | semidirect |
| 4. #20292895 | C2 | semidirect |
| 5. #20292888 | C2 | semidirect |
| 6. #20292675 | C2 | semidirect |
| 7. #20292609 | C2 | semidirect |
| 8. C2×#16812026 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C107 | C2 | semidirect |
| 12. #16812139 | C22 | semidirect |
| 16. #16812134 | C22 | semidirect |
| 18. C2×#13133806 | C22 | semidirect |
| 19. C2×#13133803 | C22 | semidirect |
| 21. #16812116 | C22 | semidirect |
| 26. #16812044 | C22 | semidirect |
| 27. #16812027 | C22 | semidirect |
| 28. #16812026 | C22 | semidirect |
| 29. #16812025 | C22 | semidirect |
| 148. C107 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293425 | 2 |
| C2×#16812135 | 2 |
| #20293394 | 2 |
| #20292895 | 2 |
| #20292888 | 2 |
| #20292675 | 2 |
| #20292609 | 2 |
| C2×#16812026 | 2 |
| C2×AGL(1,ℤ/8)×C107 | 2 |
| #3068 | 107 |