Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 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. #20293343 | C2 | semidirect |
| 2. #20293297 | C2 | semidirect |
| 3. #20292950 | C2 | semidirect |
| 4. #20292919 | C2 | semidirect |
| 5. #20292862 | C2 | semidirect |
| 6. #20292819 | C2 | semidirect |
| 7. #20292773 | C2 | semidirect |
| 8. C4×#13133807 | C2 | semidirect |
| 9. C8×D428 | C2 | semidirect |
| 10. #20292620 | C2 | semidirect |
| 11. #486×C107 | C2 | semidirect |
| 133. C107 | #3305 | semidirect |
| 136. #486 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293343 | 2 |
| #20293297 | 2 |
| #20292950 | 2 |
| #20292919 | 2 |
| #20292862 | 2 |
| #20292819 | 2 |
| #20292773 | 2 |
| C4×#13133807 | 2 |
| C8×D428 | 2 |
| #20292620 | 2 |
| #486×C107 | 2 |
| #3305 | 107 |