Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22550250 | C2 | semidirect |
| 3. #22550224 | C2 | semidirect |
| 4. C8×C127⋊C8 | C2 | semidirect |
| 5. #500×C127 | C2 | semidirect |
| 32. C127⋊C8 | D8 | semidirect |
| 38. C8×C127 | SD16 | semidirect |
| 52. C127 | #1706 | semidirect |
| 53. #500 | D127 | semidirect |
| 90. C8 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550253 | 2 |
| #22550250 | 2 |
| #22550224 | 2 |
| C8×C127⋊C8 | 2 |
| #500×C127 | 2 |
| #1706 | 127 |