Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#16813652 | C2 | semidirect |
| 2. C2×M16×D113 | C2 | semidirect |
| 4. C2×#16813602 | C2 | semidirect |
| 5. #20298855 | C2 | semidirect |
| 6. #20298843 | C2 | semidirect |
| 7. #20298838 | C2 | semidirect |
| 8. #20298826 | C2 | semidirect |
| 9. #20298638 | C2 | semidirect |
| 10. #20298608 | C2 | semidirect |
| 11. #417×C113 | C2 | semidirect |
| 15. C2×#14268637 | C22 | semidirect |
| 16. C2×#14268635 | C22 | semidirect |
| 36. #16813555 | C22 | semidirect |
| 37. #16813553 | C22 | semidirect |
| 38. #16813547 | C22 | semidirect |
| 39. #16813547 | C22 | semidirect |
| 43. #103×C113 | C22 | semidirect |
| 44. #102×C113 | C22 | semidirect |
| 62. #14268631 | D4 | semidirect |
| 145. C2×D113 | #137 | semidirect |
| 164. C113 | #3056 | semidirect |
| 175. #417 | D113 | semidirect |
| 207. #103 | C2×D113 | semidirect |
| 208. #102 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813652 | 2 |
| C2×M16×D113 | 2 |
| #20299105 | 2 |
| C2×#16813602 | 2 |
| #20298855 | 2 |
| #20298843 | 2 |
| #20298838 | 2 |
| #20298826 | 2 |
| #20298638 | 2 |
| #20298608 | 2 |
| #417×C113 | 2 |
| #3056 | 113 |