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. #22550433 | C2 | semidirect |
| 3. #22550236 | C2 | semidirect |
| 4. #22550231 | C2 | semidirect |
| 5. #22549886 | C2 | semidirect |
| 7. C4×M16×C127 | C2 | semidirect |
| 10. #16861209 | C22 | semidirect |
| 11. #16861201 | C22 | semidirect |
| 19. #16861134 | C22 | semidirect |
| 23. #97×C127 | C22 | semidirect |
| 24. C4×C8×C127 | C22 | semidirect |
| 84. C127 | #3140 | semidirect |
| 91. C4×M16 | D127 | semidirect |
| 107. #97 | C2×D127 | semidirect |
| 108. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550433 | 2 |
| C2×#16861197 | 2 |
| #22550236 | 2 |
| #22550231 | 2 |
| #22549886 | 2 |
| #22549882 | 2 |
| C4×M16×C127 | 2 |
| #3140 | 127 |