Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4×Q8×D127 | C2 | semidirect |
| 3. #22550191 | C2 | semidirect |
| 4. #22550168 | C2 | semidirect |
| 5. #22550077 | C2 | semidirect |
| 6. #22550076 | C2 | semidirect |
| 7. #22550016 | C2 | semidirect |
| 8. #22549979 | C2 | semidirect |
| 9. #22549975 | C2 | semidirect |
| 10. #22549932 | C2 | semidirect |
| 11. #477×C127 | C2 | semidirect |
| 87. Dic254 | #41 | semidirect |
| 108. Q8×C127 | #41 | semidirect |
| 141. C127 | #3112 | semidirect |
| 146. #477 | D127 | semidirect |
| 231. Q8 | #14523249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550427 | 2 |
| C4×Q8×D127 | 2 |
| #22550191 | 2 |
| #22550168 | 2 |
| #22550077 | 2 |
| #22550076 | 2 |
| #22550016 | 2 |
| #22549979 | 2 |
| #22549975 | 2 |
| #22549932 | 2 |
| #477×C127 | 2 |
| #3112 | 127 |