Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 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 |
|---|---|---|
| 1. #22550272 | C2 | semidirect |
| 4. #22550226 | C2 | semidirect |
| 6. #22549597 | C2 | semidirect |
| 7. #500×C127 | C2 | semidirect |
| 54. C8×C127 | SD16 | semidirect |
| 70. C127 | #1714 | semidirect |
| 71. #500 | D127 | semidirect |
| 124. C8 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550272 | 2 |
| #22550250 | 2 |
| #22550249 | 2 |
| #22550226 | 2 |
| #22550224 | 2 |
| #22549597 | 2 |
| #500×C127 | 2 |
| #1714 | 127 |