Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #22550284 | C2 | semidirect |
| 4. #22550283 | C2 | semidirect |
| 5. #22550278 | C2 | semidirect |
| 6. #22550275 | C2 | semidirect |
| 7. #22550275 | C2 | semidirect |
| 11. #499×C127 | C2 | semidirect |
| 43. #14523231 | Q8 | semidirect |
| 44. #14523231 | Q8 | semidirect |
| 100. C127 | #3166 | semidirect |
| 108. #499 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550432 | 2 |
| #125×D127 | 2 |
| #22550284 | 2 |
| #22550283 | 2 |
| #22550278 | 2 |
| #22550275 | 2 |
| #22549917 | 2 |
| #22549915 | 2 |
| C4×#14523231 | 2 |
| #499×C127 | 2 |
| #3166 | 127 |