Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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. C22×Dic508 | C2 | semidirect |
| 3. #22550532 | C2 | semidirect |
| 4. #22550259 | C2 | semidirect |
| 5. #22550118 | C2 | semidirect |
| 6. #22550097 | C2 | semidirect |
| 7. #22550039 | C2 | semidirect |
| 8. #22550014 | C2 | semidirect |
| 9. #22549970 | C2 | semidirect |
| 10. C8×C22⋊D127 | C2 | semidirect |
| 11. #466×C127 | C2 | semidirect |
| 55. Dic508 | D4 | semidirect |
| 116. C22×C127 | #135 | semidirect |
| 137. C127 | #3285 | semidirect |
| 143. #466 | D127 | semidirect |
| 256. C22 | #16861228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861228 | 2 |
| C22×Dic508 | 2 |
| #22550532 | 2 |
| #22550259 | 2 |
| #22550118 | 2 |
| #22550097 | 2 |
| #22550039 | 2 |
| #22550014 | 2 |
| #22549970 | 2 |
| C8×C22⋊D127 | 2 |
| #466×C127 | 2 |
| #3285 | 127 |