Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #20293351 | C2 | semidirect |
| 3. #20292966 | C2 | semidirect |
| 4. #20292904 | C2 | semidirect |
| 5. #20292867 | C2 | semidirect |
| 6. #20292834 | C2 | semidirect |
| 7. #20292792 | C2 | semidirect |
| 8. C4×#13133807 | C2 | semidirect |
| 9. C8×D428 | C2 | semidirect |
| 10. #20292622 | C2 | semidirect |
| 11. #487×C107 | C2 | semidirect |
| 126. C107 | #3302 | semidirect |
| 129. #487 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293351 | 2 |
| #20293280 | 2 |
| #20292966 | 2 |
| #20292904 | 2 |
| #20292867 | 2 |
| #20292834 | 2 |
| #20292792 | 2 |
| C4×#13133807 | 2 |
| C8×D428 | 2 |
| #20292622 | 2 |
| #487×C107 | 2 |
| #3302 | 107 |