Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20293255 | C2 | semidirect |
| 3. #20292935 | C2 | semidirect |
| 4. #20292928 | C2 | semidirect |
| 5. #20292918 | C2 | semidirect |
| 6. #20292913 | C2 | semidirect |
| 7. #20292669 | C2 | semidirect |
| 8. C2×#16812041 | C2 | semidirect |
| 11. #424×C107 | C2 | semidirect |
| 42. #13133818 | Q8 | semidirect |
| 124. C107 | #3084 | semidirect |
| 133. #424 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20293107 | 2 |
| #20292935 | 2 |
| #20292928 | 2 |
| #20292918 | 2 |
| #20292913 | 2 |
| #20292669 | 2 |
| C2×#16812041 | 2 |
| #20292629 | 2 |
| #20292624 | 2 |
| #424×C107 | 2 |
| #3084 | 107 |