Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #20293334 | C2 | semidirect |
| 3. #20293032 | C2 | semidirect |
| 4. #20292969 | C2 | semidirect |
| 5. #20292941 | C2 | semidirect |
| 6. #20292923 | C2 | semidirect |
| 7. #20292918 | C2 | semidirect |
| 8. #20292873 | C2 | semidirect |
| 9. C4×#13133807 | C2 | semidirect |
| 10. #20292669 | C2 | semidirect |
| 11. #436×C107 | C2 | semidirect |
| 122. C107 | #3357 | semidirect |
| 132. #436 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293342 | 2 |
| #20293334 | 2 |
| #20293032 | 2 |
| #20292969 | 2 |
| #20292941 | 2 |
| #20292923 | 2 |
| #20292918 | 2 |
| #20292873 | 2 |
| C4×#13133807 | 2 |
| #20292669 | 2 |
| #436×C107 | 2 |
| #3357 | 107 |