Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20293426 | C2 | semidirect |
| 2. C2×#16812132 | C2 | semidirect |
| 3. #131×D107 | C2 | semidirect |
| 4. #20292899 | C2 | semidirect |
| 5. #20292898 | C2 | semidirect |
| 6. #20292897 | C2 | semidirect |
| 7. #20292893 | C2 | semidirect |
| 8. #20292892 | C2 | semidirect |
| 9. #108×D107 | C2 | semidirect |
| 10. #20292610 | C2 | semidirect |
| 11. #473×C107 | C2 | semidirect |
| 25. C2×#13133805 | C22 | semidirect |
| 26. C2×D856 | C22 | semidirect |
| 37. #16812045 | C22 | semidirect |
| 38. #16812044 | C22 | semidirect |
| 39. #16812028 | C22 | semidirect |
| 40. #16812025 | C22 | semidirect |
| 41. #16812025 | C22 | semidirect |
| 43. C2×Q16×C107 | C22 | semidirect |
| 45. #108×C107 | C22 | semidirect |
| 46. #101×C107 | C22 | semidirect |
| 167. C107 | #3067 | semidirect |
| 172. #473 | D107 | semidirect |
| 193. C2×Q16 | C2×D107 | semidirect |
| 209. #108 | C2×D107 | semidirect |
| 211. #101 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293426 | 2 |
| C2×#16812132 | 2 |
| #131×D107 | 2 |
| #20292899 | 2 |
| #20292898 | 2 |
| #20292897 | 2 |
| #20292893 | 2 |
| #20292892 | 2 |
| #108×D107 | 2 |
| #20292610 | 2 |
| #473×C107 | 2 |
| #3067 | 107 |