Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20293435 | C2 | semidirect |
| 2. #20293429 | C2 | semidirect |
| 3. #20293012 | C2 | semidirect |
| 4. #20292899 | C2 | semidirect |
| 5. #20292897 | C2 | semidirect |
| 6. #20292892 | C2 | semidirect |
| 7. #20292803 | C2 | semidirect |
| 8. #20292800 | C2 | semidirect |
| 9. #20292744 | C2 | semidirect |
| 10. #20292742 | C2 | semidirect |
| 11. #578×C107 | C2 | semidirect |
| 18. #16812134 | C22 | semidirect |
| 23. C2×#13133805 | C22 | semidirect |
| 26. #16812116 | C22 | semidirect |
| 28. #16812098 | C22 | semidirect |
| 29. #16812045 | C22 | semidirect |
| 30. #16812044 | C22 | semidirect |
| 31. #16812036 | C22 | semidirect |
| 32. #16812036 | C22 | semidirect |
| 34. #16812028 | C22 | semidirect |
| 35. #16812025 | C22 | semidirect |
| 36. C8×Dic107 | C22 | semidirect |
| 37. 2−1+4×C107 | C22 | semidirect |
| 39. #137×C107 | C22 | semidirect |
| 43. C2×Q16×C107 | C22 | semidirect |
| 44. #131×C107 | C22 | semidirect |
| 150. C107 | #3290 | semidirect |
| 151. #578 | D107 | semidirect |
| 162. 2−1+4 | C2×D107 | semidirect |
| 167. #137 | C2×D107 | semidirect |
| 178. C2×Q16 | C2×D107 | semidirect |
| 185. #131 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293435 | 2 |
| #20293429 | 2 |
| #20293012 | 2 |
| #20292899 | 2 |
| #20292897 | 2 |
| #20292892 | 2 |
| #20292803 | 2 |
| #20292800 | 2 |
| #20292744 | 2 |
| #20292742 | 2 |
| #578×C107 | 2 |
| #3290 | 107 |