Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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. #22550305 | C2 | semidirect |
| 2. D16×D127 | C2 | semidirect |
| 3. #22549715 | C2 | semidirect |
| 4. #22549714 | C2 | semidirect |
| 5. #22549711 | C2 | semidirect |
| 6. #22549709 | C2 | semidirect |
| 7. D32×C127 | C2 | semidirect |
| 10. Dic1016 | C22 | semidirect |
| 15. C127⋊C32 | C22 | semidirect |
| 17. D16×C127 | C22 | semidirect |
| 18. C32×C127 | C22 | semidirect |
| 55. C127 | #2263 | semidirect |
| 61. D32 | D127 | semidirect |
| 70. D16 | C2×D127 | semidirect |
| 73. C32 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550305 | 2 |
| D16×D127 | 2 |
| #22549715 | 2 |
| #22549714 | 2 |
| #22549711 | 2 |
| #22549709 | 2 |
| D32×C127 | 2 |
| #2263 | 127 |