Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#16813645 | C2 | semidirect |
| 2. C2×M16×D113 | C2 | semidirect |
| 3. #20299111 | C2 | semidirect |
| 4. #20298853 | C2 | semidirect |
| 5. #20298852 | C2 | semidirect |
| 6. #20298851 | C2 | semidirect |
| 7. #20298847 | C2 | semidirect |
| 8. #20298846 | C2 | semidirect |
| 9. #20298633 | C2 | semidirect |
| 10. #20298593 | C2 | semidirect |
| 11. #470×C113 | C2 | semidirect |
| 15. C2×#14268634 | C22 | semidirect |
| 16. C2×D904 | C22 | semidirect |
| 31. #16813555 | C22 | semidirect |
| 32. #16813554 | C22 | semidirect |
| 33. #16813546 | C22 | semidirect |
| 34. #16813544 | C22 | semidirect |
| 35. #16813542 | C22 | semidirect |
| 36. C2×Q16×C113 | C22 | semidirect |
| 39. #106×C113 | C22 | semidirect |
| 40. #103×C113 | C22 | semidirect |
| 64. C8×D113 | D4 | semidirect |
| 141. C113 | #3054 | semidirect |
| 146. #470 | D113 | semidirect |
| 156. C2×Q16 | C2×D113 | semidirect |
| 177. #106 | C2×D113 | semidirect |
| 179. #103 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813645 | 2 |
| C2×M16×D113 | 2 |
| #20299111 | 2 |
| #20298853 | 2 |
| #20298852 | 2 |
| #20298851 | 2 |
| #20298847 | 2 |
| #20298846 | 2 |
| #20298633 | 2 |
| #20298593 | 2 |
| #470×C113 | 2 |
| #3054 | 113 |