Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#14268646 | C2 | semidirect |
| 2. C2×#16813652 | C2 | semidirect |
| 3. #20299105 | C2 | semidirect |
| 4. #20298757 | C2 | semidirect |
| 5. #20298740 | C2 | semidirect |
| 6. #20298608 | C2 | semidirect |
| 7. #20298603 | C2 | semidirect |
| 8. #20298561 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C113 | C2 | semidirect |
| 19. C2×#14268637 | C22 | semidirect |
| 20. C2×#14268635 | C22 | semidirect |
| 23. #16813598 | C22 | semidirect |
| 24. #16813593 | C22 | semidirect |
| 28. #16813547 | C22 | semidirect |
| 29. #16813543 | C22 | semidirect |
| 30. #16813534 | C22 | semidirect |
| 34. C2×SD16×C113 | C22 | semidirect |
| 35. C2×D8×C113 | C22 | semidirect |
| 43. C2×Dic226 | D4 | semidirect |
| 73. C2×D4×C113 | D4 | semidirect |
| 146. C113 | #3005 | semidirect |
| 149. C2×AGL(1,ℤ/8) | D113 | semidirect |
| 170. C2×SD16 | C2×D113 | semidirect |
| 171. C2×D8 | C2×D113 | semidirect |
| 201. C2×D4 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268646 | 2 |
| C2×#16813652 | 2 |
| #20299105 | 2 |
| #20298757 | 2 |
| #20298740 | 2 |
| #20298608 | 2 |
| #20298603 | 2 |
| #20298561 | 2 |
| C2×AGL(1,ℤ/8)×C113 | 2 |
| #3005 | 113 |