Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812137 | C2 | semidirect |
| 2. C22×D856 | C2 | semidirect |
| 3. #20293196 | C2 | semidirect |
| 4. #20293101 | C2 | semidirect |
| 5. #20292843 | C2 | semidirect |
| 6. #20292823 | C2 | semidirect |
| 7. #20292633 | C2 | semidirect |
| 8. #20292624 | C2 | semidirect |
| 9. #424×C107 | C2 | semidirect |
| 14. C2×#13133807 | C22 | semidirect |
| 17. C2×D856 | C22 | semidirect |
| 18. #16812106 | C22 | semidirect |
| 19. #16812097 | C22 | semidirect |
| 22. C4×D428 | C22 | semidirect |
| 26. #16812034 | C22 | semidirect |
| 27. #16812031 | C22 | semidirect |
| 28. #16812031 | C22 | semidirect |
| 32. C4⋊C8×C107 | C22 | semidirect |
| 44. C2×D428 | D4 | semidirect |
| 122. C107 | #3041 | semidirect |
| 129. #424 | D107 | semidirect |
| 151. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812137 | 2 |
| C22×D856 | 2 |
| #20293196 | 2 |
| #20293101 | 2 |
| #20292843 | 2 |
| #20292823 | 2 |
| #20292633 | 2 |
| #20292624 | 2 |
| #424×C107 | 2 |
| #3041 | 107 |