Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 2. C2×#16861217 | C2 | semidirect |
| 3. #22549997 | C2 | semidirect |
| 4. #22549992 | C2 | semidirect |
| 5. #22549892 | C2 | semidirect |
| 6. #22549834 | C2 | semidirect |
| 7. #430×C127 | C2 | semidirect |
| 9. #16861242 | C4 | semidirect |
| 10. #16861237 | C4 | semidirect |
| 14. #16861217 | C22 | semidirect |
| 15. #16861217 | C22 | semidirect |
| 20. #16861135 | C22 | semidirect |
| 21. #16861119 | C22 | semidirect |
| 22. C8×Dic127 | C22 | semidirect |
| 25. #108×C127 | C22 | semidirect |
| 90. C127 | #2955 | semidirect |
| 95. #430 | D127 | semidirect |
| 112. #108 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550676 | 2 |
| C2×#16861217 | 2 |
| #22549997 | 2 |
| #22549992 | 2 |
| #22549892 | 2 |
| #22549834 | 2 |
| #430×C127 | 2 |
| #2955 | 127 |