Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20293352 | C2 | semidirect |
| 3. #20292994 | C2 | semidirect |
| 4. #20292932 | C2 | semidirect |
| 5. #20292919 | C2 | semidirect |
| 8. #20292757 | C2 | semidirect |
| 11. #487×C107 | C2 | semidirect |
| 117. C107 | #3372 | semidirect |
| 121. #487 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293352 | 2 |
| #20293338 | 2 |
| #20292994 | 2 |
| #20292932 | 2 |
| #20292919 | 2 |
| #20292831 | 2 |
| #20292829 | 2 |
| #20292757 | 2 |
| #20292730 | 2 |
| C4×#13133807 | 2 |
| #487×C107 | 2 |
| #3372 | 107 |