Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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×#16861229 | C2 | semidirect |
| 2. C2×#16861217 | C2 | semidirect |
| 3. #22550457 | C2 | semidirect |
| 4. #22550454 | C2 | semidirect |
| 5. #22550125 | C2 | semidirect |
| 6. #22550121 | C2 | semidirect |
| 7. #22550116 | C2 | semidirect |
| 8. #22550111 | C2 | semidirect |
| 9. C2×#16861142 | C2 | semidirect |
| 10. #22549878 | C2 | semidirect |
| 11. #417×C127 | C2 | semidirect |
| 63. C2×C127⋊C8 | D4 | semidirect |
| 153. C127 | #3061 | semidirect |
| 164. #417 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861229 | 2 |
| C2×#16861217 | 2 |
| #22550457 | 2 |
| #22550454 | 2 |
| #22550125 | 2 |
| #22550121 | 2 |
| #22550116 | 2 |
| #22550111 | 2 |
| C2×#16861142 | 2 |
| #22549878 | 2 |
| #417×C127 | 2 |
| #3061 | 127 |