Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16861209 | C2 | semidirect |
| 3. #22550172 | C2 | semidirect |
| 4. #22550167 | C2 | semidirect |
| 5. #22550162 | C2 | semidirect |
| 6. #22550157 | C2 | semidirect |
| 7. #22549918 | C2 | semidirect |
| 9. #423×C127 | C2 | semidirect |
| 36. #14523248 | Q8 | semidirect |
| 74. Dic254 | C2×Q8 | semidirect |
| 76. D508 | C2×Q8 | semidirect |
| 122. C127 | #3079 | semidirect |
| 130. #423 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861209 | 2 |
| C4×#14523248 | 2 |
| #22550172 | 2 |
| #22550167 | 2 |
| #22550162 | 2 |
| #22550157 | 2 |
| #22549918 | 2 |
| #22549878 | 2 |
| #423×C127 | 2 |
| #3079 | 127 |