Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14268635 | C2 | semidirect |
| 3. #20299165 | C2 | semidirect |
| 4. #20298740 | C2 | semidirect |
| 5. #20298735 | C2 | semidirect |
| 6. #20298608 | C2 | semidirect |
| 7. #20298594 | C2 | semidirect |
| 8. #20298566 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C113 | C2 | semidirect |
| 15. C2×#14268646 | C22 | semidirect |
| 18. C2×Q8×D113 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 28. #16813546 | C22 | semidirect |
| 29. #16813543 | C22 | semidirect |
| 30. #16813534 | C22 | semidirect |
| 48. C2×Dic226 | D4 | semidirect |
| 69. #41×C113 | D4 | semidirect |
| 146. C113 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D113 | semidirect |
| 191. #41 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813669 | 2 |
| C22×#14268635 | 2 |
| #20299165 | 2 |
| #20298740 | 2 |
| #20298735 | 2 |
| #20298608 | 2 |
| #20298594 | 2 |
| #20298566 | 2 |
| C2×AGL(1,ℤ/8)×C113 | 2 |
| #3010 | 113 |