Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#16861231 | C2 | semidirect |
| 2. #22550312 | C2 | direct (N × H) |
| 3. C2×#16861153 | C2 | semidirect |
| 4. C2×#16861150 | C2 | semidirect |
| 5. C2×#16861149 | C2 | semidirect |
| 6. C22×D8×C127 | C2 | semidirect |
| 9. #16861231 | C22 | semidirect |
| 10. C2×Dic508 | C22 | semidirect |
| 12. C2×D1016 | C22 | semidirect |
| 13. #16861153 | C22 | semidirect |
| 14. #16861150 | C22 | semidirect |
| 15. #16861149 | C22 | semidirect |
| 16. C2×C127⋊C16 | C22 | semidirect |
| 21. C2×D8×C127 | C22 | semidirect |
| 30. Dic508 | C23 | semidirect |
| 33. D1016 | C23 | semidirect |
| 34. C127⋊C16 | C23 | semidirect |
| 84. C2×C127 | #509 | semidirect |
| 88. C127 | C2×#509 | semidirect |
| 90. C22×D8 | D127 | semidirect |
| 105. C2×D8 | C2×D127 | semidirect |
| 173. C2 | #22550312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| #22550312 | 2 |
| C2×#16861153 | 2 |
| C2×#16861150 | 2 |
| C2×#16861149 | 2 |
| C22×D8×C127 | 2 |
| C2×#509 | 127 |