Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20293184 | C2 | semidirect |
| 3. #20293036 | C2 | semidirect |
| 4. #20293021 | C2 | semidirect |
| 5. #20292996 | C2 | semidirect |
| 6. #20292987 | C2 | semidirect |
| 7. #20292885 | C2 | semidirect |
| 9. C4×Dic428 | C2 | semidirect |
| 10. C4×#13133807 | C2 | semidirect |
| 11. C4×M16×C107 | C2 | semidirect |
| 130. C107 | #3172 | semidirect |
| 141. C4×M16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| #20293161 | 2 |
| #20293036 | 2 |
| #20293021 | 2 |
| #20292996 | 2 |
| #20292987 | 2 |
| #20292885 | 2 |
| #20292873 | 2 |
| C4×Dic428 | 2 |
| C4×#13133807 | 2 |
| C4×M16×C107 | 2 |
| #3172 | 107 |