Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22550604 | C2 | semidirect |
| 3. #22550227 | C2 | semidirect |
| 4. #22550225 | C2 | semidirect |
| 5. #22550161 | C2 | semidirect |
| 6. #22550160 | C2 | semidirect |
| 9. C8×Dic254 | C2 | semidirect |
| 78. Dic254 | SD16 | semidirect |
| 119. C127 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550604 | 2 |
| D4×Dic254 | 2 |
| #22550227 | 2 |
| #22550225 | 2 |
| #22550161 | 2 |
| #22550160 | 2 |
| #22550081 | 2 |
| #22550079 | 2 |
| C8×Dic254 | 2 |
| #22549967 | 2 |
| C4×SD16×C127 | 2 |
| #3359 | 127 |