Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20293427 | C2 | semidirect |
| 2. C2×#16812135 | C2 | semidirect |
| 3. C2×#16812135 | C2 | semidirect |
| 4. #20293393 | C2 | semidirect |
| 5. #20292896 | C2 | semidirect |
| 6. #20292889 | C2 | semidirect |
| 7. #20292675 | C2 | semidirect |
| 8. #20292609 | C2 | semidirect |
| 9. C2×#100×C107 | C2 | semidirect |
| 13. #16812142 | C22 | semidirect |
| 15. #16812137 | C22 | semidirect |
| 22. C2×#13133806 | C22 | semidirect |
| 24. C2×#13133803 | C22 | semidirect |
| 25. #16812117 | C22 | semidirect |
| 30. #16812044 | C22 | semidirect |
| 31. #16812027 | C22 | semidirect |
| 32. #16812025 | C22 | semidirect |
| 36. #100×C107 | C22 | semidirect |
| 148. C107 | #3068 | semidirect |
| 157. C2×#100 | D107 | semidirect |
| 184. #100 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293427 | 2 |
| C2×#16812135 | 2 |
| #20293393 | 2 |
| #20292896 | 2 |
| #20292889 | 2 |
| #20292675 | 2 |
| #20292609 | 2 |
| C2×#100×C107 | 2 |
| #3068 | 107 |