Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20292904 | C2 | semidirect |
| 3. #20292706 | C2 | semidirect |
| 4. #20292380 | C2 | semidirect |
| 5. #20292373 | C2 | semidirect |
| 6. #20292371 | C2 | semidirect |
| 7. #492×C107 | C2 | semidirect |
| 62. C8×C107 | D8 | semidirect |
| 86. C107 | #1685 | semidirect |
| 87. #492 | D107 | semidirect |
| 151. C8 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292904 | 2 |
| #20292819 | 2 |
| #20292706 | 2 |
| #20292380 | 2 |
| #20292373 | 2 |
| #20292371 | 2 |
| #492×C107 | 2 |
| #1685 | 107 |