Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20293255 | C2 | semidirect |
| 3. #20292992 | C2 | semidirect |
| 4. #20292987 | C2 | semidirect |
| 5. #20292982 | C2 | semidirect |
| 6. #20292974 | C2 | semidirect |
| 7. #20292633 | C2 | semidirect |
| 8. #20292629 | C2 | semidirect |
| 9. #20292624 | C2 | semidirect |
| 10. C2×#16812031 | C2 | semidirect |
| 11. #405×C107 | C2 | semidirect |
| 14. #16812109 | C22 | semidirect |
| 17. #16812101 | C22 | semidirect |
| 26. #16812034 | C22 | semidirect |
| 27. #16812034 | C22 | semidirect |
| 28. #16812034 | C22 | semidirect |
| 33. #16812031 | C22 | semidirect |
| 34. #16812031 | C22 | semidirect |
| 35. #16812031 | C22 | semidirect |
| 39. #97×C107 | C22 | semidirect |
| 40. C4×C8×C107 | C22 | semidirect |
| 136. C107 | #3136 | semidirect |
| 147. #405 | D107 | semidirect |
| 175. #97 | C2×D107 | semidirect |
| 176. C4×C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20293196 | 2 |
| #20292992 | 2 |
| #20292987 | 2 |
| #20292982 | 2 |
| #20292974 | 2 |
| #20292633 | 2 |
| #20292629 | 2 |
| #20292624 | 2 |
| C2×#16812031 | 2 |
| #405×C107 | 2 |
| #3136 | 107 |