Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #20293334 | C2 | semidirect |
| 2. #20293297 | C2 | semidirect |
| 3. #20292990 | C2 | semidirect |
| 4. #20292973 | C2 | semidirect |
| 5. #20292929 | C2 | semidirect |
| 6. #20292918 | C2 | semidirect |
| 7. #20292820 | C2 | semidirect |
| 8. #20292754 | C2 | semidirect |
| 9. #20292739 | C2 | semidirect |
| 10. C4×#13133803 | C2 | semidirect |
| 11. #459×C107 | C2 | semidirect |
| 82. D4×C107 | #41 | semidirect |
| 130. C107 | #3366 | semidirect |
| 138. #459 | D107 | semidirect |
| 218. D4 | #13133817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293334 | 2 |
| #20293297 | 2 |
| #20292990 | 2 |
| #20292973 | 2 |
| #20292929 | 2 |
| #20292918 | 2 |
| #20292820 | 2 |
| #20292754 | 2 |
| #20292739 | 2 |
| C4×#13133803 | 2 |
| #459×C107 | 2 |
| #3366 | 107 |