Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
924 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. C2×#16861171 | C2 | semidirect |
| 3. #22549777 | C2 | semidirect |
| 4. C42×Dic127 | C2 | semidirect |
| 5. #384×C127 | C2 | semidirect |
| 8. #16861206 | C4 | semidirect |
| 18. C2×D508 | C2×C4 | semidirect |
| 24. C4×Dic127 | D4 | semidirect |
| 28. C42×C127 | C2×C4 | semidirect |
| 49. C4×C127 | C4×D4 | semidirect |
| 51. Dic127 | #127 | semidirect |
| 57. C127 | C4×#127 | semidirect |
| 61. #384 | D127 | semidirect |
| 85. C42 | C4×D127 | semidirect |
| 108. C4 | #16861171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861206 | 2 |
| C2×#16861171 | 2 |
| #22549777 | 2 |
| C42×Dic127 | 2 |
| #384×C127 | 2 |
| C4×#127 | 127 |