Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #20293363 | C2 | semidirect |
| 2. #20293338 | C2 | semidirect |
| 3. #20292980 | C2 | semidirect |
| 4. #20292929 | C2 | semidirect |
| 5. #20292919 | C2 | semidirect |
| 6. #20292841 | C2 | semidirect |
| 8. C8×Dic214 | C2 | semidirect |
| 9. C4×#13133807 | C2 | semidirect |
| 10. #20292707 | C2 | semidirect |
| 11. #486×C107 | C2 | semidirect |
| 123. C107 | #3361 | semidirect |
| 127. #486 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293363 | 2 |
| #20293338 | 2 |
| #20292980 | 2 |
| #20292929 | 2 |
| #20292919 | 2 |
| #20292841 | 2 |
| #20292819 | 2 |
| C8×Dic214 | 2 |
| C4×#13133807 | 2 |
| #20292707 | 2 |
| #486×C107 | 2 |
| #3361 | 107 |