Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16813669 | C2 | semidirect |
| 2. #20299398 | C2 | semidirect |
| 3. #20299396 | C2 | semidirect |
| 4. #20299174 | C2 | semidirect |
| 5. #20298782 | C2 | semidirect |
| 6. #20298772 | C2 | semidirect |
| 7. #20298616 | C2 | semidirect |
| 8. C2×#16813540 | C2 | semidirect |
| 9. #421×C113 | C2 | semidirect |
| 23. #16813655 | C22 | semidirect |
| 25. #16813652 | C22 | semidirect |
| 27. #16813650 | C22 | semidirect |
| 29. #16813647 | C22 | semidirect |
| 33. #16813622 | C22 | semidirect |
| 34. #16813610 | C22 | semidirect |
| 37. #16813550 | C22 | semidirect |
| 38. #16813540 | C22 | semidirect |
| 42. #104×C113 | C22 | semidirect |
| 186. C113 | #3020 | semidirect |
| 194. #421 | D113 | semidirect |
| 227. #104 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813669 | 2 |
| #20299398 | 2 |
| #20299396 | 2 |
| #20299174 | 2 |
| #20298782 | 2 |
| #20298772 | 2 |
| #20298616 | 2 |
| C2×#16813540 | 2 |
| #421×C113 | 2 |
| #3020 | 113 |