Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16812128 | C2 | semidirect |
| 2. C22×Dic428 | C2 | semidirect |
| 3. #20293283 | C2 | semidirect |
| 4. #20293010 | C2 | semidirect |
| 5. #20292869 | C2 | semidirect |
| 6. #20292848 | C2 | semidirect |
| 7. #20292790 | C2 | semidirect |
| 8. #20292765 | C2 | semidirect |
| 9. #20292721 | C2 | semidirect |
| 10. C8×C22⋊D107 | C2 | semidirect |
| 11. #466×C107 | C2 | semidirect |
| 55. Dic428 | D4 | semidirect |
| 116. C22×C107 | #135 | semidirect |
| 137. C107 | #3285 | semidirect |
| 143. #466 | D107 | semidirect |
| 256. C22 | #16812128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812128 | 2 |
| C22×Dic428 | 2 |
| #20293283 | 2 |
| #20293010 | 2 |
| #20292869 | 2 |
| #20292848 | 2 |
| #20292790 | 2 |
| #20292765 | 2 |
| #20292721 | 2 |
| C8×C22⋊D107 | 2 |
| #466×C107 | 2 |
| #3285 | 107 |