Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20293357 | C2 | semidirect |
| 3. #20292972 | C2 | semidirect |
| 4. #20292915 | C2 | semidirect |
| 5. #20292914 | C2 | semidirect |
| 6. #20292826 | C2 | semidirect |
| 7. #20292824 | C2 | semidirect |
| 8. C8×Dic214 | C2 | semidirect |
| 9. #20292718 | C2 | semidirect |
| 10. C4×#13133807 | C2 | semidirect |
| 11. #486×C107 | C2 | semidirect |
| 98. Dic214 | SD16 | semidirect |
| 99. Dic214 | #41 | semidirect |
| 126. C107 | #3362 | semidirect |
| 130. #486 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293357 | 2 |
| #20293297 | 2 |
| #20292972 | 2 |
| #20292915 | 2 |
| #20292914 | 2 |
| #20292826 | 2 |
| #20292824 | 2 |
| C8×Dic214 | 2 |
| #20292718 | 2 |
| C4×#13133807 | 2 |
| #486×C107 | 2 |
| #3362 | 107 |