Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20293297 | C2 | semidirect |
| 2. D4×Dic214 | C2 | semidirect |
| 3. #20292973 | C2 | semidirect |
| 4. #20292972 | C2 | semidirect |
| 5. #20292908 | C2 | semidirect |
| 6. #20292905 | C2 | semidirect |
| 7. #20292820 | C2 | semidirect |
| 8. #20292751 | C2 | semidirect |
| 9. D8×Dic107 | C2 | semidirect |
| 10. C4×#13133803 | C2 | semidirect |
| 11. #459×C107 | C2 | semidirect |
| 83. D4×C107 | #41 | semidirect |
| 102. Dic214 | D8 | semidirect |
| 132. C107 | #3358 | semidirect |
| 140. #459 | D107 | semidirect |
| 222. D4 | #13133817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293297 | 2 |
| D4×Dic214 | 2 |
| #20292973 | 2 |
| #20292972 | 2 |
| #20292908 | 2 |
| #20292905 | 2 |
| #20292820 | 2 |
| #20292751 | 2 |
| D8×Dic107 | 2 |
| C4×#13133803 | 2 |
| #459×C107 | 2 |
| #3358 | 107 |