Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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. #22549743 | C2 | semidirect |
| 3. #22549742 | C2 | semidirect |
| 6. C4⋊C4×Dic127 | C2 | semidirect |
| 8. #22549721 | C2 | semidirect |
| 9. #382×C127 | C2 | semidirect |
| 19. C42×D127 | C4 | semidirect |
| 106. C127 | #2283 | semidirect |
| 110. #382 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D127 | 2 |
| #22549743 | 2 |
| #22549742 | 2 |
| #22549738 | 2 |
| #22549733 | 2 |
| C4⋊C4×Dic127 | 2 |
| #22549723 | 2 |
| #22549721 | 2 |
| #382×C127 | 2 |
| #2283 | 127 |