Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #20292582 | C2 | semidirect |
| 5. #20292399 | C2 | semidirect |
| 6. #20292397 | C2 | semidirect |
| 7. #405×C107 | C2 | semidirect |
| 15. C2×#13133801 | C4 | semidirect |
| 16. C2×C8×D107 | C4 | semidirect |
| 18. #16812027 | C4 | semidirect |
| 19. #16812025 | C4 | semidirect |
| 107. C107 | #1757 | semidirect |
| 112. #405 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812115 | 2 |
| #20292609 | 2 |
| #20292600 | 2 |
| #20292582 | 2 |
| #20292399 | 2 |
| #20292397 | 2 |
| #405×C107 | 2 |
| #1757 | 107 |