Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D452 | C2 | semidirect |
| 2. C2×#16813650 | C2 | semidirect |
| 3. #20299109 | C2 | semidirect |
| 4. #20298751 | C2 | semidirect |
| 5. #20298734 | C2 | semidirect |
| 6. #20298604 | C2 | semidirect |
| 7. #407×C113 | C2 | semidirect |
| 9. C2×#14268647 | C22 | semidirect |
| 16. C2×#14268636 | C22 | semidirect |
| 17. C2×D904 | C22 | semidirect |
| 19. #16813601 | C22 | semidirect |
| 20. #16813596 | C22 | semidirect |
| 23. #16813581 | C22 | semidirect |
| 24. #16813544 | C22 | semidirect |
| 26. C2×M16×C113 | C22 | semidirect |
| 27. C22⋊C8×C113 | C22 | semidirect |
| 33. C2×Dic226 | C23 | semidirect |
| 40. C2×D452 | D4 | semidirect |
| 42. C2×D452 | C23 | semidirect |
| 48. C4⋊Dic113 | C23 | semidirect |
| 61. C2×C8×C113 | C23 | semidirect |
| 98. C22×C113 | AGL(1,ℤ/8) | semidirect |
| 118. C113 | #3003 | semidirect |
| 125. #407 | D113 | semidirect |
| 137. C2×M16 | C2×D113 | semidirect |
| 145. C22⋊C8 | C2×D113 | semidirect |
| 173. C2×C8 | C22×D113 | semidirect |
| 222. C22 | #16813650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D452 | 2 |
| C2×#16813650 | 2 |
| #20299109 | 2 |
| #20298751 | 2 |
| #20298734 | 2 |
| #20298604 | 2 |
| #407×C113 | 2 |
| #3003 | 113 |