Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22551585 | C2 | semidirect |
| 2. #22551585 | C2 | semidirect |
| 3. #22551578 | C2 | semidirect |
| 4. #22551576 | C2 | semidirect |
| 5. #22551575 | C2 | semidirect |
| 6. #22551574 | C2 | semidirect |
| 7. #22551571 | C2 | semidirect |
| 8. #22551569 | C2 | semidirect |
| 10. C4×C22⋊D257 | C2 | semidirect |
| 11. #22551552 | C2 | semidirect |
| 12. #22551551 | C2 | semidirect |
| 13. #22551548 | C2 | semidirect |
| 14. C2×C22⋊Dic257 | C2 | semidirect |
| 15. C2×C22⋊C4×C257 | C2 | semidirect |
| 16. C2×Dic514 | C22 | semidirect |
| 22. C2×C4×D257 | C22 | semidirect |
| 23. C4⋊Dic257 | C22 | semidirect |
| 24. C4⋊Dic257 | C22 | semidirect |
| 25. C4⋊Dic257 | C22 | semidirect |
| 26. #16861597 | C22 | semidirect |
| 27. #16861597 | C22 | semidirect |
| 28. #16861597 | C22 | semidirect |
| 29. #16861597 | C22 | semidirect |
| 30. #16861597 | C22 | semidirect |
| 38. #16861595 | C22 | semidirect |
| 39. #16861595 | C22 | semidirect |
| 40. #16861595 | C22 | semidirect |
| 41. C4×Dic257 | C22 | semidirect |
| 42. C4×Dic257 | C22 | semidirect |
| 43. C4×Dic257 | C22 | semidirect |
| 110. C257 | #551 | semidirect |
| 126. C2×C22⋊C4 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551585 | 2 |
| #22551578 | 2 |
| #22551576 | 2 |
| #22551575 | 2 |
| #22551574 | 2 |
| #22551571 | 2 |
| #22551569 | 2 |
| #22551561 | 2 |
| C4×C22⋊D257 | 2 |
| #22551552 | 2 |
| #22551551 | 2 |
| #22551548 | 2 |
| C2×C22⋊Dic257 | 2 |
| C2×C22⋊C4×C257 | 2 |
| #551 | 257 |