Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
180 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22549953 | C2 | semidirect |
| 3. #22549603 | C2 | semidirect |
| 4. C8×C127⋊C8 | C2 | semidirect |
| 5. #335×C127 | C2 | semidirect |
| 37. C127⋊C8 | D8 | semidirect |
| 43. C8×C127 | M16 | semidirect |
| 59. C127 | #1589 | semidirect |
| 62. #335 | D127 | semidirect |
| 102. C8 | #14523231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1016 | 2 |
| #22549953 | 2 |
| #22549603 | 2 |
| C8×C127⋊C8 | 2 |
| #335×C127 | 2 |
| #1589 | 127 |