Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20293158 | C2 | semidirect |
| 2. #20293028 | C2 | semidirect |
| 3. #20293010 | C2 | semidirect |
| 4. #20292980 | C2 | semidirect |
| 5. #20292868 | C2 | semidirect |
| 6. #20292854 | C2 | semidirect |
| 7. #20292721 | C2 | semidirect |
| 8. #20292718 | C2 | semidirect |
| 9. D8×Dic107 | C2 | semidirect |
| 10. C2×C8×Dic107 | C2 | semidirect |
| 119. C107 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293158 | 2 |
| #20293028 | 2 |
| #20293010 | 2 |
| #20292980 | 2 |
| #20292868 | 2 |
| #20292854 | 2 |
| #20292721 | 2 |
| #20292718 | 2 |
| D8×Dic107 | 2 |
| C2×C8×Dic107 | 2 |
| #466×C107 | 2 |
| #3168 | 107 |