Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×Q16×D127 | C2 | semidirect |
| 4. #22550255 | C2 | semidirect |
| 5. #22550116 | C2 | semidirect |
| 6. #22550087 | C2 | semidirect |
| 7. #22550033 | C2 | semidirect |
| 8. #22550030 | C2 | semidirect |
| 9. C4×#14523238 | C2 | semidirect |
| 11. #462×C127 | C2 | semidirect |
| 57. #14523238 | D4 | semidirect |
| 89. D508 | Q16 | semidirect |
| 114. C2×D127 | C2×Q16 | semidirect |
| 119. C4×C127 | C2×Q16 | semidirect |
| 131. C127 | D4×Q16 | semidirect |
| 138. #462 | D127 | semidirect |
| 254. C4 | Q16×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D127 | 2 |
| Q8×D508 | 2 |
| #22550541 | 2 |
| #22550255 | 2 |
| #22550116 | 2 |
| #22550087 | 2 |
| #22550033 | 2 |
| #22550030 | 2 |
| C4×#14523238 | 2 |
| #22549941 | 2 |
| #462×C127 | 2 |
| D4×Q16 | 127 |