Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
382 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 382 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. #22550604 | C2 | semidirect |
| 3. #22550241 | C2 | semidirect |
| 4. #22550223 | C2 | semidirect |
| 5. #22550177 | C2 | semidirect |
| 6. #22550157 | C2 | semidirect |
| 7. #22550077 | C2 | semidirect |
| 8. #22550077 | C2 | semidirect |
| 9. #22549978 | C2 | semidirect |
| 10. C4×#14523237 | C2 | semidirect |
| 11. #446×C127 | C2 | semidirect |
| 78. Dic254 | #41 | semidirect |
| 125. C127 | #3368 | semidirect |
| 134. #446 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550604 | 2 |
| #22550548 | 2 |
| #22550241 | 2 |
| #22550223 | 2 |
| #22550177 | 2 |
| #22550157 | 2 |
| #22550077 | 2 |
| #22549978 | 2 |
| C4×#14523237 | 2 |
| #446×C127 | 2 |
| #3368 | 127 |