Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22550432 | C2 | semidirect |
| 3. #22550244 | C2 | semidirect |
| 4. #22550242 | C2 | semidirect |
| 5. #22550241 | C2 | semidirect |
| 6. #22550237 | C2 | semidirect |
| 7. #22549871 | C2 | semidirect |
| 8. #97×D127 | C2 | semidirect |
| 9. #491×C127 | C2 | semidirect |
| 91. C127 | #3135 | semidirect |
| 95. #491 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550432 | 2 |
| #22550427 | 2 |
| #22550244 | 2 |
| #22550242 | 2 |
| #22550241 | 2 |
| #22550237 | 2 |
| #22549871 | 2 |
| #97×D127 | 2 |
| #491×C127 | 2 |
| #3135 | 127 |