Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
182 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20293001 | C2 | semidirect |
| 3. #20292705 | C2 | semidirect |
| 4. #20292379 | C2 | semidirect |
| 5. #20292373 | C2 | semidirect |
| 6. #20292370 | C2 | semidirect |
| 7. #474×C107 | C2 | semidirect |
| 65. C107⋊C8 | D8 | semidirect |
| 86. C107 | #1685 | semidirect |
| 88. #474 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293001 | 2 |
| #20292822 | 2 |
| #20292705 | 2 |
| #20292379 | 2 |
| #20292373 | 2 |
| #20292370 | 2 |
| #474×C107 | 2 |
| #1685 | 107 |