Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
512 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 2. #22549775 | C2 | semidirect |
| 3. #22549769 | C2 | semidirect |
| 4. #22549769 | C2 | semidirect |
| 5. #22549762 | C2 | semidirect |
| 7. #22549751 | C2 | semidirect |
| 8. #22549736 | C2 | semidirect |
| 28. #123×C127 | C4 | semidirect |
| 55. C22×C4×C127 | C2×C4 | semidirect |
| 59. C4⋊C4×C127 | C2×C4 | semidirect |
| 61. C22⋊C4×C127 | C2×C4 | semidirect |
| 127. C127 | #2376 | semidirect |
| 140. #123 | Dic127 | semidirect |
| 172. C22×C4 | C2×Dic127 | semidirect |
| 180. C4⋊C4 | C2×Dic127 | semidirect |
| 186. C22⋊C4 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549779 | 2 |
| #22549775 | 2 |
| #22549769 | 2 |
| #22549762 | 2 |
| #22549756 | 2 |
| #22549751 | 2 |
| #22549736 | 2 |
| C2×#123×C127 | 2 |
| #2376 | 127 |