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. C22×Dic508 | C2 | semidirect |
| 2. C2×Q16×D127 | C2 | semidirect |
| 4. #22550254 | C2 | semidirect |
| 5. #22550118 | C2 | semidirect |
| 6. #22550085 | C2 | semidirect |
| 7. #22550033 | C2 | semidirect |
| 8. #22550031 | C2 | semidirect |
| 9. #22549970 | C2 | semidirect |
| 11. #467×C127 | C2 | semidirect |
| 55. Dic508 | D4 | semidirect |
| 87. C22⋊D127 | Q16 | semidirect |
| 112. C22×C127 | C2×Q16 | semidirect |
| 116. C2×D127 | C2×Q16 | semidirect |
| 126. Dic127 | C2×Q16 | semidirect |
| 133. C127 | D4×Q16 | semidirect |
| 139. #467 | D127 | semidirect |
| 248. C22 | Q16×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic508 | 2 |
| C2×Q16×D127 | 2 |
| #22550539 | 2 |
| #22550254 | 2 |
| #22550118 | 2 |
| #22550085 | 2 |
| #22550033 | 2 |
| #22550031 | 2 |
| #22549970 | 2 |
| C8×C22⋊D127 | 2 |
| #467×C127 | 2 |
| D4×Q16 | 127 |