Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 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. #20293347 | C2 | semidirect |
| 2. #20293334 | C2 | semidirect |
| 3. #20292980 | C2 | semidirect |
| 4. #20292978 | C2 | semidirect |
| 5. #20292933 | C2 | semidirect |
| 6. #20292917 | C2 | semidirect |
| 8. #20292832 | C2 | semidirect |
| 9. C8×Dic214 | C2 | semidirect |
| 10. #20292718 | C2 | semidirect |
| 121. C107 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293347 | 2 |
| #20293334 | 2 |
| #20292980 | 2 |
| #20292978 | 2 |
| #20292933 | 2 |
| #20292917 | 2 |
| #20292840 | 2 |
| #20292832 | 2 |
| C8×Dic214 | 2 |
| #20292718 | 2 |
| C4×D8×C107 | 2 |
| #3360 | 107 |