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. #20293298 | C2 | semidirect |
| 3. #20292990 | C2 | semidirect |
| 4. #20292974 | C2 | semidirect |
| 5. #20292930 | C2 | semidirect |
| 6. #20292917 | C2 | semidirect |
| 7. #20292822 | C2 | semidirect |
| 8. #20292820 | C2 | semidirect |
| 9. #20292757 | C2 | semidirect |
| 10. #20292736 | C2 | semidirect |
| 11. C4×D8×C107 | C2 | semidirect |
| 80. D4×C107 | #41 | semidirect |
| 130. C107 | #3366 | semidirect |
| 141. C4×D8 | D107 | semidirect |
| 218. D4 | #13133818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293334 | 2 |
| #20293298 | 2 |
| #20292990 | 2 |
| #20292974 | 2 |
| #20292930 | 2 |
| #20292917 | 2 |
| #20292822 | 2 |
| #20292820 | 2 |
| #20292757 | 2 |
| #20292736 | 2 |
| C4×D8×C107 | 2 |
| #3366 | 107 |