Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #20292928 | C2 | semidirect |
| 4. #20292928 | C2 | semidirect |
| 5. #20292918 | C2 | semidirect |
| 6. #20292908 | C2 | semidirect |
| 7. #20292669 | C2 | semidirect |
| 8. #20292665 | C2 | semidirect |
| 11. #424×C107 | C2 | semidirect |
| 13. #16812109 | C22 | semidirect |
| 15. #16812101 | C22 | semidirect |
| 26. #16812043 | C22 | semidirect |
| 27. #16812043 | C22 | semidirect |
| 28. #16812043 | C22 | semidirect |
| 29. #16812041 | C22 | semidirect |
| 30. #16812041 | C22 | semidirect |
| 31. #16812041 | C22 | semidirect |
| 39. C4⋊C8×C107 | C22 | semidirect |
| 40. C4⋊C8×C107 | C22 | semidirect |
| 45. C2×D428 | Q8 | semidirect |
| 125. C107 | #3081 | semidirect |
| 134. #424 | D107 | semidirect |
| 160. C4⋊C8 | C2×D107 | semidirect |
| 161. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20293101 | 2 |
| #20292928 | 2 |
| #20292918 | 2 |
| #20292908 | 2 |
| #20292669 | 2 |
| #20292665 | 2 |
| #20292633 | 2 |
| C2×#16812031 | 2 |
| #424×C107 | 2 |
| #3081 | 107 |