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. C22×D1016 | C2 | semidirect |
| 3. #22550314 | C2 | direct (N × H) |
| 4. C2×#16861154 | C2 | semidirect |
| 5. C2×D2032 | C2 | semidirect |
| 6. C2×M32×C127 | C2 | semidirect |
| 10. #16861231 | C22 | semidirect |
| 11. C2×Dic508 | C22 | semidirect |
| 16. C2×D1016 | C22 | semidirect |
| 17. C2×D1016 | C22 | semidirect |
| 18. #16861154 | C22 | semidirect |
| 19. D2032 | C22 | semidirect |
| 21. M32×C127 | C22 | semidirect |
| 22. C2×C16×C127 | C22 | semidirect |
| 35. Dic508 | C23 | semidirect |
| 41. D1016 | C23 | semidirect |
| 47. C16×C127 | C23 | semidirect |
| 83. C2×C127 | #509 | semidirect |
| 88. C127 | C2×#509 | semidirect |
| 94. C2×M32 | D127 | semidirect |
| 109. M32 | C2×D127 | semidirect |
| 110. C2×C16 | C2×D127 | semidirect |
| 135. C16 | C22×D127 | semidirect |
| 173. C2 | #22550314 | 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 |
| C22×D1016 | 2 |
| #22550314 | 2 |
| C2×#16861154 | 2 |
| C2×D2032 | 2 |
| C2×M32×C127 | 2 |
| C2×#509 | 127 |