Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16812133 | C2 | semidirect |
| 2. #20293175 | C2 | semidirect |
| 3. C4×D4×D107 | C2 | semidirect |
| 4. #20292841 | C2 | semidirect |
| 5. #20292840 | C2 | semidirect |
| 6. #20292833 | C2 | semidirect |
| 7. #20292832 | C2 | semidirect |
| 8. #20292819 | C2 | semidirect |
| 9. #20292649 | C2 | semidirect |
| 10. #20292625 | C2 | semidirect |
| 11. #459×C107 | C2 | semidirect |
| 20. #16812109 | C22 | semidirect |
| 21. #16812096 | C22 | semidirect |
| 34. C4⋊(C107⋊C8) | C22 | semidirect |
| 35. Dic107⋊C8 | C22 | semidirect |
| 36. #16812034 | C22 | semidirect |
| 37. #16812032 | C22 | semidirect |
| 38. #16812030 | C22 | semidirect |
| 40. #127×C107 | C22 | semidirect |
| 42. C4⋊C8×C107 | C22 | semidirect |
| 43. #102×C107 | C22 | semidirect |
| 52. D4×D107 | D4 | semidirect |
| 145. C4×C107 | AGL(1,ℤ/8) | semidirect |
| 161. C107 | #3036 | semidirect |
| 170. #459 | D107 | semidirect |
| 183. #127 | C2×D107 | semidirect |
| 200. C4⋊C8 | C2×D107 | semidirect |
| 204. #102 | C2×D107 | semidirect |
| 311. C4 | #16812133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812133 | 2 |
| #20293175 | 2 |
| C4×D4×D107 | 2 |
| #20292841 | 2 |
| #20292840 | 2 |
| #20292833 | 2 |
| #20292832 | 2 |
| #20292819 | 2 |
| #20292649 | 2 |
| #20292625 | 2 |
| #459×C107 | 2 |
| #3036 | 107 |