Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813630 | C2 | semidirect |
| 2. #20299176 | C2 | semidirect |
| 3. #20299165 | C2 | semidirect |
| 4. #20298848 | C2 | semidirect |
| 5. #20298841 | C2 | semidirect |
| 6. #20298831 | C2 | semidirect |
| 7. #20298824 | C2 | semidirect |
| 8. #20298640 | C2 | semidirect |
| 9. #20298594 | C2 | semidirect |
| 10. C2×#16813543 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C113 | C2 | semidirect |
| 14. C2×#14268630 | C22 | semidirect |
| 16. C2×C8×D113 | C22 | semidirect |
| 20. #16813598 | C22 | semidirect |
| 25. #16813593 | C22 | semidirect |
| 29. #16813556 | C22 | semidirect |
| 30. #16813554 | C22 | semidirect |
| 31. #16813546 | C22 | semidirect |
| 32. #16813546 | C22 | semidirect |
| 35. #16813543 | C22 | semidirect |
| 36. #16813543 | C22 | semidirect |
| 83. M16×C113 | D4 | semidirect |
| 152. C113 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D113 | semidirect |
| 220. M16 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813630 | 2 |
| #20299176 | 2 |
| #20299165 | 2 |
| #20298848 | 2 |
| #20298841 | 2 |
| #20298831 | 2 |
| #20298824 | 2 |
| #20298640 | 2 |
| #20298594 | 2 |
| C2×#16813543 | 2 |
| C2×AGL(1,ℤ/8)×C113 | 2 |
| #3062 | 113 |