Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. C4×#14523248 | C2 | semidirect |
| 2. #22550197 | C2 | semidirect |
| 3. #22550158 | C2 | semidirect |
| 4. #22550153 | C2 | semidirect |
| 5. #22550073 | C2 | semidirect |
| 6. #22550068 | C2 | semidirect |
| 7. #22550019 | C2 | semidirect |
| 8. #22549986 | C2 | semidirect |
| 9. #22549976 | C2 | semidirect |
| 10. #22549933 | C2 | semidirect |
| 11. #532×C127 | C2 | semidirect |
| 85. Dic254 | #41 | semidirect |
| 87. D508 | #41 | semidirect |
| 145. C127 | #3115 | semidirect |
| 146. #532 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523248 | 2 |
| #22550197 | 2 |
| #22550158 | 2 |
| #22550153 | 2 |
| #22550073 | 2 |
| #22550068 | 2 |
| #22550019 | 2 |
| #22549986 | 2 |
| #22549976 | 2 |
| #22549933 | 2 |
| #532×C127 | 2 |
| #3115 | 127 |