Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #22550642 | C2 | semidirect |
| 3. #22549997 | C2 | semidirect |
| 4. #22549992 | C2 | semidirect |
| 5. C2×#16861135 | C2 | semidirect |
| 6. M16×Dic127 | C2 | semidirect |
| 7. #430×C127 | C2 | semidirect |
| 9. #16861242 | C4 | semidirect |
| 10. #16861237 | C4 | semidirect |
| 12. #16861217 | C22 | semidirect |
| 17. #16861135 | C22 | semidirect |
| 18. #16861135 | C22 | semidirect |
| 19. #16861119 | C22 | semidirect |
| 20. C8×Dic127 | C22 | semidirect |
| 23. #108×C127 | C22 | semidirect |
| 33. Dic508 | C2×C4 | semidirect |
| 34. #14523237 | C2×C4 | semidirect |
| 35. D1016 | C2×C4 | semidirect |
| 86. C127 | #2956 | semidirect |
| 91. #430 | D127 | semidirect |
| 105. #108 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550676 | 2 |
| #22550642 | 2 |
| #22549997 | 2 |
| #22549992 | 2 |
| C2×#16861135 | 2 |
| M16×Dic127 | 2 |
| #430×C127 | 2 |
| #2956 | 127 |