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. #20293425 | C2 | semidirect |
| 2. C2×#16812137 | C2 | semidirect |
| 3. C2×#16812134 | C2 | semidirect |
| 4. #20293393 | C2 | semidirect |
| 5. #20292896 | C2 | semidirect |
| 6. #20292893 | C2 | semidirect |
| 7. #20292675 | C2 | semidirect |
| 8. C2×#16812025 | C2 | semidirect |
| 9. #413×C107 | C2 | semidirect |
| 12. #16812140 | C22 | semidirect |
| 16. #16812135 | C22 | semidirect |
| 22. C2×#13133805 | C22 | semidirect |
| 24. C2×#13133803 | C22 | semidirect |
| 25. #16812117 | C22 | semidirect |
| 30. #16812044 | C22 | semidirect |
| 31. #16812025 | C22 | semidirect |
| 35. #101×C107 | C22 | semidirect |
| 36. #100×C107 | C22 | semidirect |
| 148. C107 | #3068 | semidirect |
| 156. #413 | D107 | semidirect |
| 182. #101 | C2×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 |
|---|---|
| #20293425 | 2 |
| C2×#16812137 | 2 |
| C2×#16812134 | 2 |
| #20293393 | 2 |
| #20292896 | 2 |
| #20292893 | 2 |
| #20292675 | 2 |
| C2×#16812025 | 2 |
| #413×C107 | 2 |
| #3068 | 107 |