Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#16813650 | C2 | semidirect |
| 2. #20299176 | C2 | semidirect |
| 3. #20299162 | C2 | semidirect |
| 4. #20298851 | C2 | semidirect |
| 5. #20298844 | C2 | semidirect |
| 6. #20298834 | C2 | semidirect |
| 7. #20298827 | C2 | semidirect |
| 8. #20298640 | C2 | semidirect |
| 9. #20298595 | C2 | semidirect |
| 10. C2×#16813544 | C2 | semidirect |
| 11. C2×#131×C113 | C2 | semidirect |
| 19. #16813601 | C22 | semidirect |
| 23. #16813596 | C22 | semidirect |
| 29. #16813556 | C22 | semidirect |
| 30. #16813554 | C22 | semidirect |
| 31. #16813547 | C22 | semidirect |
| 32. #16813547 | C22 | semidirect |
| 35. #16813544 | C22 | semidirect |
| 36. #16813544 | C22 | semidirect |
| 40. C2×M16×C113 | C22 | semidirect |
| 42. C22×C8×C113 | C22 | semidirect |
| 79. M16×C113 | D4 | semidirect |
| 152. C113 | #3062 | semidirect |
| 154. C2×#131 | D113 | semidirect |
| 172. C2×M16 | C2×D113 | semidirect |
| 174. C22×C8 | C2×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×#16813650 | 2 |
| #20299176 | 2 |
| #20299162 | 2 |
| #20298851 | 2 |
| #20298844 | 2 |
| #20298834 | 2 |
| #20298827 | 2 |
| #20298640 | 2 |
| #20298595 | 2 |
| C2×#16813544 | 2 |
| C2×#131×C113 | 2 |
| #3062 | 113 |