Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D127 | C2 | semidirect |
| 3. #22550171 | C2 | semidirect |
| 4. #22550167 | C2 | semidirect |
| 5. #22550163 | C2 | semidirect |
| 6. #22550159 | C2 | semidirect |
| 7. #22550155 | C2 | semidirect |
| 8. #22549917 | C2 | semidirect |
| 9. #22549898 | C2 | semidirect |
| 11. #477×C127 | C2 | semidirect |
| 44. #14523249 | Q8 | semidirect |
| 88. D508 | C2×Q8 | semidirect |
| 105. Q8×C127 | C2×Q8 | semidirect |
| 138. C127 | #3079 | semidirect |
| 142. #477 | D127 | semidirect |
| 226. Q8 | Q8×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D127 | 2 |
| C4×#14523249 | 2 |
| #22550171 | 2 |
| #22550167 | 2 |
| #22550163 | 2 |
| #22550159 | 2 |
| #22550155 | 2 |
| #22549917 | 2 |
| #22549898 | 2 |
| #22549876 | 2 |
| #477×C127 | 2 |
| #3079 | 127 |