Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20293423 | C2 | semidirect |
| 2. C2×#16812128 | C2 | semidirect |
| 3. #131×D107 | C2 | semidirect |
| 4. #20292903 | C2 | semidirect |
| 5. #20292902 | C2 | semidirect |
| 6. #20292894 | C2 | semidirect |
| 7. #20292889 | C2 | semidirect |
| 8. #20292888 | C2 | semidirect |
| 9. #108×D107 | C2 | semidirect |
| 10. #20292608 | C2 | semidirect |
| 11. #472×C107 | C2 | semidirect |
| 25. C2×Dic428 | C22 | semidirect |
| 26. C2×#13133806 | C22 | semidirect |
| 37. #16812045 | C22 | semidirect |
| 38. #16812044 | C22 | semidirect |
| 39. #16812027 | C22 | semidirect |
| 40. #16812027 | C22 | semidirect |
| 41. #16812026 | C22 | semidirect |
| 43. C2×D8×C107 | C22 | semidirect |
| 45. #108×C107 | C22 | semidirect |
| 46. #100×C107 | C22 | semidirect |
| 167. C107 | #3067 | semidirect |
| 174. #472 | D107 | semidirect |
| 195. C2×D8 | C2×D107 | semidirect |
| 209. #108 | C2×D107 | semidirect |
| 213. #100 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293423 | 2 |
| C2×#16812128 | 2 |
| #131×D107 | 2 |
| #20292903 | 2 |
| #20292902 | 2 |
| #20292894 | 2 |
| #20292889 | 2 |
| #20292888 | 2 |
| #108×D107 | 2 |
| #20292608 | 2 |
| #472×C107 | 2 |
| #3067 | 107 |