Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#16812116 | C2 | semidirect |
| 2. #20292749 | C2 | semidirect |
| 3. #20292744 | C2 | semidirect |
| 4. #20292676 | C2 | semidirect |
| 5. #20292644 | C2 | semidirect |
| 6. #20292585 | C2 | semidirect |
| 10. #16812116 | C22 | semidirect |
| 11. #16812116 | C22 | semidirect |
| 17. #16812045 | C22 | semidirect |
| 18. #16812036 | C22 | semidirect |
| 19. #16812019 | C22 | semidirect |
| 20. C8×Dic107 | C22 | semidirect |
| 22. #137×C107 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C107 | C4 | semidirect |
| 90. C107 | #2955 | semidirect |
| 99. #137 | Dic107 | semidirect |
| 100. AGL(1,ℤ/8) | Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812116 | 2 |
| #20292749 | 2 |
| #20292744 | 2 |
| #20292676 | 2 |
| #20292644 | 2 |
| #20292585 | 2 |
| #575×C107 | 2 |
| #2955 | 107 |