Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16861230 | C2 | semidirect |
| 2. C2×#16861228 | C2 | semidirect |
| 3. #22550425 | C2 | semidirect |
| 4. #22550424 | C2 | semidirect |
| 5. #22550271 | C2 | semidirect |
| 6. #22550270 | C2 | semidirect |
| 7. #22550267 | C2 | semidirect |
| 8. #22550264 | C2 | semidirect |
| 9. #22550263 | C2 | semidirect |
| 10. #97×D127 | C2 | semidirect |
| 11. #496×C127 | C2 | semidirect |
| 64. C8×D127 | D4 | semidirect |
| 134. C127 | #3150 | semidirect |
| 144. #496 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861230 | 2 |
| C2×#16861228 | 2 |
| #22550425 | 2 |
| #22550424 | 2 |
| #22550271 | 2 |
| #22550270 | 2 |
| #22550267 | 2 |
| #22550264 | 2 |
| #22550263 | 2 |
| #97×D127 | 2 |
| #496×C127 | 2 |
| #3150 | 127 |