Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22550076 | C2 | semidirect |
| 3. #22549629 | C2 | semidirect |
| 4. #22549619 | C2 | semidirect |
| 5. C8×Q8×C127 | C2 | semidirect |
| 40. Q8×C127 | D8 | semidirect |
| 48. C8×C127 | SD16 | semidirect |
| 65. C127 | #1668 | semidirect |
| 68. C8×Q8 | D127 | semidirect |
| 99. Q8 | D1016 | semidirect |
| 113. C8 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550253 | 2 |
| #22550076 | 2 |
| #22549629 | 2 |
| #22549619 | 2 |
| C8×Q8×C127 | 2 |
| #1668 | 127 |