Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. #20293342 | C2 | semidirect |
| 2. #20293023 | C2 | semidirect |
| 3. #20292948 | C2 | semidirect |
| 4. #20292945 | C2 | semidirect |
| 5. #20292917 | C2 | semidirect |
| 6. #20292904 | C2 | semidirect |
| 7. #20292878 | C2 | semidirect |
| 8. C4×#13133803 | C2 | semidirect |
| 9. #20292705 | C2 | semidirect |
| 10. #20292667 | C2 | semidirect |
| 11. #547×C107 | C2 | semidirect |
| 101. C107⋊C8 | #41 | semidirect |
| 128. C107 | #3354 | semidirect |
| 130. #547 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293342 | 2 |
| #20293023 | 2 |
| #20292948 | 2 |
| #20292945 | 2 |
| #20292917 | 2 |
| #20292904 | 2 |
| #20292878 | 2 |
| C4×#13133803 | 2 |
| #20292705 | 2 |
| #20292667 | 2 |
| #547×C107 | 2 |
| #3354 | 107 |