Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22550224 | C2 | semidirect |
| 3. D4×C127⋊C8 | C2 | semidirect |
| 4. #22549628 | C2 | semidirect |
| 5. #22549622 | C2 | semidirect |
| 6. #22549619 | C2 | semidirect |
| 7. #461×C127 | C2 | semidirect |
| 85. C127 | #1681 | semidirect |
| 87. #461 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550224 | 2 |
| #22550071 | 2 |
| D4×C127⋊C8 | 2 |
| #22549628 | 2 |
| #22549622 | 2 |
| #22549619 | 2 |
| #461×C127 | 2 |
| #1681 | 127 |