Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #20293363 | C2 | semidirect |
| 2. #20293297 | C2 | semidirect |
| 3. #20293015 | C2 | semidirect |
| 4. #20292840 | C2 | semidirect |
| 5. #20292824 | C2 | semidirect |
| 6. #20292820 | C2 | semidirect |
| 7. #20292819 | C2 | semidirect |
| 8. #20292757 | C2 | semidirect |
| 9. #20292739 | C2 | semidirect |
| 10. C4×#13133807 | C2 | semidirect |
| 11. #493×C107 | C2 | semidirect |
| 107. C8×C107 | #41 | semidirect |
| 135. C107 | #3399 | semidirect |
| 139. #493 | D107 | semidirect |
| 243. C8 | #13133817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293363 | 2 |
| #20293297 | 2 |
| #20293015 | 2 |
| #20292840 | 2 |
| #20292824 | 2 |
| #20292820 | 2 |
| #20292819 | 2 |
| #20292757 | 2 |
| #20292739 | 2 |
| C4×#13133807 | 2 |
| #493×C107 | 2 |
| #3399 | 107 |