Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
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. #22548708 | C2 | semidirect |
| 2. #22548708 | C2 | semidirect |
| 3. #22548701 | C2 | semidirect |
| 4. #22548699 | C2 | semidirect |
| 5. #22548698 | C2 | semidirect |
| 6. #22548697 | C2 | semidirect |
| 7. #22548694 | C2 | semidirect |
| 8. #22548692 | C2 | semidirect |
| 10. C4×C22⋊D251 | C2 | semidirect |
| 11. (C22⋊D251)⋊C4 | C2 | semidirect |
| 12. #22548674 | C2 | semidirect |
| 13. #22548671 | C2 | semidirect |
| 14. C2×C22⋊Dic251 | C2 | semidirect |
| 15. C2×C22⋊C4×C251 | C2 | semidirect |
| 16. C2×Dic502 | C22 | semidirect |
| 22. C2×C4×D251 | C22 | semidirect |
| 23. C4⋊Dic251 | C22 | semidirect |
| 24. C4⋊Dic251 | C22 | semidirect |
| 25. C4⋊Dic251 | C22 | semidirect |
| 26. Dic251⋊C4 | C22 | semidirect |
| 27. Dic251⋊C4 | C22 | semidirect |
| 28. Dic251⋊C4 | C22 | semidirect |
| 29. Dic251⋊C4 | C22 | semidirect |
| 30. Dic251⋊C4 | C22 | semidirect |
| 38. (C2×D251)⋊C4 | C22 | semidirect |
| 39. (C2×D251)⋊C4 | C22 | semidirect |
| 40. (C2×D251)⋊C4 | C22 | semidirect |
| 41. C4×Dic251 | C22 | semidirect |
| 42. C4×Dic251 | C22 | semidirect |
| 43. C4×Dic251 | C22 | semidirect |
| 110. C251 | #551 | semidirect |
| 126. C2×C22⋊C4 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22548708 | 2 |
| #22548701 | 2 |
| #22548699 | 2 |
| #22548698 | 2 |
| #22548697 | 2 |
| #22548694 | 2 |
| #22548692 | 2 |
| #22548684 | 2 |
| C4×C22⋊D251 | 2 |
| (C22⋊D251)⋊C4 | 2 |
| #22548674 | 2 |
| #22548671 | 2 |
| C2×C22⋊Dic251 | 2 |
| C2×C22⋊C4×C251 | 2 |
| #551 | 251 |