Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22550427 | C2 | semidirect |
| 2. #22550423 | C2 | semidirect |
| 3. #22550165 | C2 | semidirect |
| 4. #22550163 | C2 | semidirect |
| 5. #22550130 | C2 | semidirect |
| 6. #22550128 | C2 | semidirect |
| 7. #22550072 | C2 | semidirect |
| 8. #22550071 | C2 | semidirect |
| 9. #22550070 | C2 | semidirect |
| 10. #22549898 | C2 | semidirect |
| 11. #476×C127 | C2 | semidirect |
| 151. C127 | #3253 | semidirect |
| 156. #476 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550427 | 2 |
| #22550423 | 2 |
| #22550165 | 2 |
| #22550163 | 2 |
| #22550130 | 2 |
| #22550128 | 2 |
| #22550072 | 2 |
| #22550071 | 2 |
| #22550070 | 2 |
| #22549898 | 2 |
| #476×C127 | 2 |
| #3253 | 127 |