Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22550600 | C2 | semidirect |
| 3. #22550213 | C2 | semidirect |
| 4. #22550203 | C2 | semidirect |
| 5. #22550158 | C2 | semidirect |
| 6. #22550153 | C2 | semidirect |
| 7. #22550123 | C2 | semidirect |
| 8. C4×#14523237 | C2 | semidirect |
| 9. #22549955 | C2 | semidirect |
| 10. #22549917 | C2 | semidirect |
| 11. #500×C127 | C2 | semidirect |
| 99. C8×C127 | #41 | semidirect |
| 123. C127 | #3353 | semidirect |
| 126. #500 | D127 | semidirect |
| 222. C8 | #14523249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550600 | 2 |
| #22550529 | 2 |
| #22550213 | 2 |
| #22550203 | 2 |
| #22550158 | 2 |
| #22550153 | 2 |
| #22550123 | 2 |
| C4×#14523237 | 2 |
| #22549955 | 2 |
| #22549917 | 2 |
| #500×C127 | 2 |
| #3353 | 127 |