Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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. Q8×C127⋊C8 | C2 | semidirect |
| 4. #22549628 | C2 | semidirect |
| 6. #22549597 | C2 | semidirect |
| 7. Q8⋊C8×C127 | C2 | semidirect |
| 53. Q8×C127 | M16 | semidirect |
| 78. C127 | #1588 | semidirect |
| 83. Q8⋊C8 | D127 | semidirect |
| 121. Q8 | #14523231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C127⋊C8 | 2 |
| C4×#14523235 | 2 |
| #22549953 | 2 |
| #22549628 | 2 |
| #22549605 | 2 |
| #22549597 | 2 |
| Q8⋊C8×C127 | 2 |
| #1588 | 127 |