Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #22549832 | C2 | semidirect |
| 5. C2×C4×C127⋊C8 | C2 | semidirect |
| 6. #22549640 | C2 | semidirect |
| 7. #339×C127 | C2 | semidirect |
| 10. #16861217 | C4 | semidirect |
| 16. #16861137 | C4 | semidirect |
| 17. #16861132 | C4 | semidirect |
| 18. #16861129 | C4 | semidirect |
| 99. C127 | #1764 | semidirect |
| 106. #339 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861217 | 2 |
| C2×#16861137 | 2 |
| #22549870 | 2 |
| #22549832 | 2 |
| C2×C4×C127⋊C8 | 2 |
| #22549640 | 2 |
| #339×C127 | 2 |
| #1764 | 127 |