Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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×#16861228 | C2 | semidirect |
| 2. C2×Q16×D127 | C2 | semidirect |
| 3. #22550534 | C2 | semidirect |
| 4. #22550114 | C2 | semidirect |
| 5. #22550109 | C2 | semidirect |
| 6. #22550095 | C2 | semidirect |
| 7. #22550035 | C2 | semidirect |
| 8. #22550013 | C2 | semidirect |
| 9. C4×Dic508 | C2 | semidirect |
| 10. C8×D508 | C2 | semidirect |
| 11. #495×C127 | C2 | semidirect |
| 54. Dic508 | D4 | semidirect |
| 120. C2×D127 | #135 | semidirect |
| 137. C127 | #3285 | semidirect |
| 141. #495 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861228 | 2 |
| C2×Q16×D127 | 2 |
| #22550534 | 2 |
| #22550114 | 2 |
| #22550109 | 2 |
| #22550095 | 2 |
| #22550035 | 2 |
| #22550013 | 2 |
| C4×Dic508 | 2 |
| C8×D508 | 2 |
| #495×C127 | 2 |
| #3285 | 127 |