Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. #20299081 | C2 | semidirect |
| 3. #20298604 | C2 | semidirect |
| 4. #20298600 | C2 | semidirect |
| 5. #20298595 | C2 | semidirect |
| 6. C2×#16813544 | C2 | semidirect |
| 7. C2×#131×C113 | C2 | semidirect |
| 9. #16813668 | C4 | semidirect |
| 16. #16813581 | C22 | semidirect |
| 17. C2×C4⋊Dic113 | C22 | semidirect |
| 18. #16813547 | C22 | semidirect |
| 19. #16813547 | C22 | semidirect |
| 20. #16813544 | C22 | semidirect |
| 21. #16813544 | C22 | semidirect |
| 22. #16813544 | C22 | semidirect |
| 25. C2×M16×C113 | C22 | semidirect |
| 26. C22×C8×C113 | C22 | semidirect |
| 30. #14268647 | C2×C4 | semidirect |
| 34. C2×D452 | C2×C4 | semidirect |
| 98. C113 | #2897 | semidirect |
| 100. C2×#131 | D113 | semidirect |
| 114. C2×M16 | C2×D113 | semidirect |
| 115. C22×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813668 | 2 |
| #20299081 | 2 |
| #20298604 | 2 |
| #20298600 | 2 |
| #20298595 | 2 |
| C2×#16813544 | 2 |
| C2×#131×C113 | 2 |
| #2897 | 113 |