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×#16861231 | C2 | semidirect |
| 2. C2×Q16×D127 | C2 | semidirect |
| 3. #22550536 | C2 | semidirect |
| 4. #22550261 | C2 | semidirect |
| 5. #22550113 | C2 | semidirect |
| 6. #22550101 | C2 | semidirect |
| 7. #22550036 | C2 | semidirect |
| 8. #22550016 | C2 | semidirect |
| 9. #22549970 | C2 | semidirect |
| 10. C8×C22⋊D127 | C2 | semidirect |
| 11. #467×C127 | C2 | semidirect |
| 54. Dic508 | D4 | semidirect |
| 120. C2×D127 | #135 | semidirect |
| 137. C127 | #3285 | semidirect |
| 142. #467 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| C2×Q16×D127 | 2 |
| #22550536 | 2 |
| #22550261 | 2 |
| #22550113 | 2 |
| #22550101 | 2 |
| #22550036 | 2 |
| #22550016 | 2 |
| #22549970 | 2 |
| C8×C22⋊D127 | 2 |
| #467×C127 | 2 |
| #3285 | 127 |