Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8×C127⋊C8 | C2 | semidirect |
| 4. #22549628 | C2 | semidirect |
| 5. #22549620 | C2 | semidirect |
| 6. #22549619 | C2 | semidirect |
| 7. #460×C127 | C2 | semidirect |
| 52. C127⋊C8 | SD16 | semidirect |
| 55. Q8×C127 | D8 | semidirect |
| 87. C127 | #1668 | semidirect |
| 90. #460 | D127 | semidirect |
| 133. Q8 | #14523233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550252 | 2 |
| #22550076 | 2 |
| Q8×C127⋊C8 | 2 |
| #22549628 | 2 |
| #22549620 | 2 |
| #22549619 | 2 |
| #460×C127 | 2 |
| #1668 | 127 |