Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D127 | C2 | semidirect |
| 4. #22550133 | C2 | semidirect |
| 5. #22550132 | C2 | semidirect |
| 6. #22550118 | C2 | semidirect |
| 7. #22550117 | C2 | semidirect |
| 8. #22550114 | C2 | semidirect |
| 9. #22549913 | C2 | semidirect |
| 10. #22549883 | C2 | semidirect |
| 11. #467×C127 | C2 | semidirect |
| 138. C127 | #3059 | semidirect |
| 147. #467 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D127 | 2 |
| C2×#16861215 | 2 |
| #22550449 | 2 |
| #22550133 | 2 |
| #22550132 | 2 |
| #22550118 | 2 |
| #22550117 | 2 |
| #22550114 | 2 |
| #22549913 | 2 |
| #22549883 | 2 |
| #467×C127 | 2 |
| #3059 | 127 |