Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20293184 | C2 | semidirect |
| 3. #20292928 | C2 | semidirect |
| 4. #20292918 | C2 | semidirect |
| 5. #20292908 | C2 | semidirect |
| 6. #20292669 | C2 | semidirect |
| 8. #423×C107 | C2 | semidirect |
| 11. #16812109 | C22 | semidirect |
| 12. #16812109 | C22 | semidirect |
| 13. #16812101 | C22 | semidirect |
| 25. #16812043 | C22 | semidirect |
| 26. #16812041 | C22 | semidirect |
| 31. C4⋊C8×C107 | C22 | semidirect |
| 32. C4⋊C8×C107 | C22 | semidirect |
| 38. C2×D428 | Q8 | semidirect |
| 116. C107 | #3077 | semidirect |
| 123. #423 | D107 | semidirect |
| 145. C4⋊C8 | C2×D107 | semidirect |
| 146. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| C2×C4×D428 | 2 |
| #20292928 | 2 |
| #20292918 | 2 |
| #20292908 | 2 |
| #20292669 | 2 |
| #20292633 | 2 |
| #423×C107 | 2 |
| #3077 | 107 |