Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22550413 | C2 | semidirect |
| 2. #22550277 | C2 | semidirect |
| 3. #22550261 | C2 | semidirect |
| 4. #22550232 | C2 | semidirect |
| 5. #22550114 | C2 | semidirect |
| 7. #22550108 | C2 | semidirect |
| 8. C4×#14523235 | C2 | semidirect |
| 9. C4×D1016 | C2 | semidirect |
| 10. C4×C8×D127 | C2 | semidirect |
| 11. C4×Q16×C127 | C2 | semidirect |
| 119. C127 | #3168 | semidirect |
| 127. C4×Q16 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550413 | 2 |
| #22550277 | 2 |
| #22550261 | 2 |
| #22550232 | 2 |
| #22550114 | 2 |
| #22550113 | 2 |
| #22550108 | 2 |
| C4×#14523235 | 2 |
| C4×D1016 | 2 |
| C4×C8×D127 | 2 |
| C4×Q16×C127 | 2 |
| #3168 | 127 |