Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20293351 | C2 | semidirect |
| 3. #20292964 | C2 | semidirect |
| 4. #20292954 | C2 | semidirect |
| 5. #20292909 | C2 | semidirect |
| 6. #20292904 | C2 | semidirect |
| 7. #20292874 | C2 | semidirect |
| 8. C4×#13133807 | C2 | semidirect |
| 9. #20292706 | C2 | semidirect |
| 10. #20292668 | C2 | semidirect |
| 11. #500×C107 | C2 | semidirect |
| 98. C8×C107 | #41 | semidirect |
| 123. C107 | #3353 | semidirect |
| 126. #500 | D107 | semidirect |
| 222. C8 | #13133819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293351 | 2 |
| #20293280 | 2 |
| #20292964 | 2 |
| #20292954 | 2 |
| #20292909 | 2 |
| #20292904 | 2 |
| #20292874 | 2 |
| C4×#13133807 | 2 |
| #20292706 | 2 |
| #20292668 | 2 |
| #500×C107 | 2 |
| #3353 | 107 |