Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299078 | C2 | semidirect |
| 3. #20298921 | C2 | semidirect |
| 4. #20298920 | C2 | semidirect |
| 5. #20298915 | C2 | semidirect |
| 6. #20298910 | C2 | semidirect |
| 7. #20298640 | C2 | semidirect |
| 8. #20298634 | C2 | semidirect |
| 9. C2×#16813543 | C2 | semidirect |
| 10. #20298566 | C2 | semidirect |
| 11. #418×C113 | C2 | semidirect |
| 23. #16813580 | C22 | semidirect |
| 25. C4⋊C4×D113 | C22 | semidirect |
| 26. #16813556 | C22 | semidirect |
| 27. #16813555 | C22 | semidirect |
| 28. #16813555 | C22 | semidirect |
| 29. #16813554 | C22 | semidirect |
| 30. #16813553 | C22 | semidirect |
| 31. #16813553 | C22 | semidirect |
| 34. #16813534 | C22 | semidirect |
| 35. #16813534 | C22 | semidirect |
| 135. C113 | #3096 | semidirect |
| 144. #418 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299165 | 2 |
| #20299078 | 2 |
| #20298921 | 2 |
| #20298920 | 2 |
| #20298915 | 2 |
| #20298910 | 2 |
| #20298640 | 2 |
| #20298634 | 2 |
| C2×#16813543 | 2 |
| #20298566 | 2 |
| #418×C113 | 2 |
| #3096 | 113 |