Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20293352 | C2 | semidirect |
| 4. #20292932 | C2 | semidirect |
| 7. #20292834 | C2 | semidirect |
| 8. C8×Dic214 | C2 | semidirect |
| 9. #20292719 | C2 | semidirect |
| 11. #487×C107 | C2 | semidirect |
| 116. C107 | #3364 | semidirect |
| 120. #487 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293352 | 2 |
| #20293351 | 2 |
| #20292983 | 2 |
| #20292932 | 2 |
| #20292904 | 2 |
| #20292852 | 2 |
| #20292834 | 2 |
| C8×Dic214 | 2 |
| #20292719 | 2 |
| C4×#13133807 | 2 |
| #487×C107 | 2 |
| #3364 | 107 |