Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22550431 | C2 | semidirect |
| 3. #22550272 | C2 | semidirect |
| 4. #22550248 | C2 | semidirect |
| 5. #22550227 | C2 | semidirect |
| 6. #22550104 | C2 | semidirect |
| 7. #22549967 | C2 | semidirect |
| 8. C4×C8×D127 | C2 | semidirect |
| 9. #486×C127 | C2 | semidirect |
| 79. C4×D127 | SD16 | semidirect |
| 80. C127⋊C8 | #41 | semidirect |
| 113. C127 | #3167 | semidirect |
| 119. #486 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550431 | 2 |
| #22550424 | 2 |
| #22550272 | 2 |
| #22550248 | 2 |
| #22550227 | 2 |
| #22550104 | 2 |
| #22549967 | 2 |
| C4×C8×D127 | 2 |
| #486×C127 | 2 |
| #3167 | 127 |