Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22550596 | C2 | semidirect |
| 3. #22550281 | C2 | semidirect |
| 4. #22550212 | C2 | semidirect |
| 5. #22550201 | C2 | semidirect |
| 6. #22550162 | C2 | semidirect |
| 7. #22550157 | C2 | semidirect |
| 8. #22550122 | C2 | semidirect |
| 9. C4×#14523237 | C2 | semidirect |
| 10. #22549918 | C2 | semidirect |
| 11. #436×C127 | C2 | semidirect |
| 99. C8×C127 | #41 | semidirect |
| 123. C127 | #3353 | semidirect |
| 133. #436 | D127 | semidirect |
| 222. C8 | #14523247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550596 | 2 |
| #22550530 | 2 |
| #22550281 | 2 |
| #22550212 | 2 |
| #22550201 | 2 |
| #22550162 | 2 |
| #22550157 | 2 |
| #22550122 | 2 |
| C4×#14523237 | 2 |
| #22549918 | 2 |
| #436×C127 | 2 |
| #3353 | 127 |