Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22550681 | C2 | semidirect |
| 2. #22550314 | C2 | semidirect |
| 3. #22550308 | C2 | semidirect |
| 4. C2×D2032 | C2 | semidirect |
| 5. #504×C127 | C2 | semidirect |
| 8. #16861231 | C22 | semidirect |
| 9. C2×D1016 | C22 | semidirect |
| 10. Dic1016 | C22 | semidirect |
| 11. #16861154 | C22 | semidirect |
| 12. D2032 | C22 | semidirect |
| 13. D2032 | C22 | semidirect |
| 15. M32×C127 | C22 | semidirect |
| 16. C2×C16×C127 | C22 | semidirect |
| 51. C127 | #3415 | semidirect |
| 56. #504 | D127 | semidirect |
| 66. M32 | C2×D127 | semidirect |
| 67. C2×C16 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550681 | 2 |
| #22550314 | 2 |
| #22550308 | 2 |
| C2×D2032 | 2 |
| #504×C127 | 2 |
| #3415 | 127 |