Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 3. #22549629 | C2 | semidirect |
| 4. #22549622 | C2 | semidirect |
| 5. #500×C127 | C2 | semidirect |
| 46. C8×C127 | SD16 | semidirect |
| 63. C127 | #1673 | semidirect |
| 64. #500 | D127 | semidirect |
| 109. C8 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550078 | 2 |
| C8×D508 | 2 |
| #22549629 | 2 |
| #22549622 | 2 |
| #500×C127 | 2 |
| #1673 | 127 |