Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
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. #20299397 | C2 | semidirect |
| 2. C2×#16813645 | C2 | semidirect |
| 3. #131×D113 | C2 | semidirect |
| 4. #20298870 | C2 | semidirect |
| 5. #20298869 | C2 | semidirect |
| 6. #20298868 | C2 | semidirect |
| 7. #20298864 | C2 | semidirect |
| 8. #20298863 | C2 | semidirect |
| 9. #108×D113 | C2 | semidirect |
| 10. #20298581 | C2 | semidirect |
| 11. #473×C113 | C2 | semidirect |
| 25. C2×#14268634 | C22 | semidirect |
| 26. C2×D904 | C22 | semidirect |
| 37. #16813558 | C22 | semidirect |
| 38. #16813557 | C22 | semidirect |
| 39. #16813541 | C22 | semidirect |
| 40. #16813538 | C22 | semidirect |
| 41. #16813538 | C22 | semidirect |
| 43. C2×Q16×C113 | C22 | semidirect |
| 45. #108×C113 | C22 | semidirect |
| 46. #101×C113 | C22 | semidirect |
| 167. C113 | #3067 | semidirect |
| 172. #473 | D113 | semidirect |
| 193. C2×Q16 | C2×D113 | semidirect |
| 209. #108 | C2×D113 | semidirect |
| 211. #101 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299397 | 2 |
| C2×#16813645 | 2 |
| #131×D113 | 2 |
| #20298870 | 2 |
| #20298869 | 2 |
| #20298868 | 2 |
| #20298864 | 2 |
| #20298863 | 2 |
| #108×D113 | 2 |
| #20298581 | 2 |
| #473×C113 | 2 |
| #3067 | 113 |