Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22550601 | C2 | semidirect |
| 3. #22550225 | C2 | semidirect |
| 4. #22550159 | C2 | semidirect |
| 5. #22550158 | C2 | semidirect |
| 8. C8×Dic254 | C2 | semidirect |
| 11. #487×C127 | C2 | semidirect |
| 78. Dic254 | SD16 | semidirect |
| 119. C127 | #3359 | semidirect |
| 123. #487 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550601 | 2 |
| #22550541 | 2 |
| #22550225 | 2 |
| #22550159 | 2 |
| #22550158 | 2 |
| #22550080 | 2 |
| #22550078 | 2 |
| C8×Dic254 | 2 |
| C4×#14523237 | 2 |
| #22549961 | 2 |
| #487×C127 | 2 |
| #3359 | 127 |