Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #20293104 | C2 | semidirect |
| 4. #20292726 | C2 | semidirect |
| 5. #20292714 | C2 | semidirect |
| 6. #20292635 | C2 | semidirect |
| 8. #20292582 | C2 | semidirect |
| 9. #427×C107 | C2 | semidirect |
| 12. C2×#13133807 | C4 | semidirect |
| 17. #16812074 | C22 | semidirect |
| 23. #16812032 | C22 | semidirect |
| 25. #16812019 | C22 | semidirect |
| 26. C8×Dic107 | C22 | semidirect |
| 30. #107×C107 | C22 | semidirect |
| 31. #106×C107 | C22 | semidirect |
| 35. C2×Dic214 | C2×C4 | semidirect |
| 43. #13133807 | C2×C4 | semidirect |
| 44. #13133807 | C2×C4 | semidirect |
| 54. C2×C8×C107 | C2×C4 | semidirect |
| 104. C107 | #2949 | semidirect |
| 110. #427 | D107 | semidirect |
| 130. #107 | C2×D107 | semidirect |
| 131. #106 | C2×D107 | semidirect |
| 152. C2×C8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133807 | 2 |
| #20293104 | 2 |
| #20293101 | 2 |
| #20292726 | 2 |
| #20292714 | 2 |
| #20292635 | 2 |
| #20292631 | 2 |
| #20292582 | 2 |
| #427×C107 | 2 |
| #2949 | 107 |