Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20293428 | C2 | semidirect |
| 2. #20292894 | C2 | semidirect |
| 3. #20292794 | C2 | semidirect |
| 4. #20292745 | C2 | semidirect |
| 5. #493×C107 | C2 | semidirect |
| 6. #16812154 | C22 | semidirect |
| 7. #16812135 | C22 | semidirect |
| 12. #16812115 | C22 | semidirect |
| 13. #16812045 | C22 | semidirect |
| 14. #16812037 | C22 | semidirect |
| 15. #16812026 | C22 | semidirect |
| 16. C2×D8×C107 | C22 | semidirect |
| 17. #127×C107 | C22 | semidirect |
| 18. C4×C8×C107 | C22 | semidirect |
| 23. Dic428 | D4 | semidirect |
| 24. #13133807 | D4 | semidirect |
| 26. D856 | D4 | semidirect |
| 65. C107 | #3292 | semidirect |
| 67. #493 | D107 | semidirect |
| 77. C2×D8 | C2×D107 | semidirect |
| 79. #127 | C2×D107 | semidirect |
| 83. C4×C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293428 | 2 |
| #20292894 | 2 |
| #20292794 | 2 |
| #20292745 | 2 |
| #493×C107 | 2 |
| #3292 | 107 |