Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22550606 | C2 | semidirect |
| 3. #22550221 | C2 | semidirect |
| 4. #22550164 | C2 | semidirect |
| 5. #22550163 | C2 | semidirect |
| 6. #22550075 | C2 | semidirect |
| 7. #22550073 | C2 | semidirect |
| 8. C8×Dic254 | C2 | semidirect |
| 9. #22549967 | C2 | semidirect |
| 10. C4×#14523237 | C2 | semidirect |
| 11. #486×C127 | C2 | semidirect |
| 77. Dic254 | SD16 | semidirect |
| 78. Dic254 | #41 | semidirect |
| 126. C127 | #3362 | semidirect |
| 130. #486 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550606 | 2 |
| #22550546 | 2 |
| #22550221 | 2 |
| #22550164 | 2 |
| #22550163 | 2 |
| #22550075 | 2 |
| #22550073 | 2 |
| C8×Dic254 | 2 |
| #22549967 | 2 |
| C4×#14523237 | 2 |
| #486×C127 | 2 |
| #3362 | 127 |