Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#16861166 | C2 | semidirect |
| 3. C2×C4⋊C4×D127 | C2 | semidirect |
| 4. #22549783 | C2 | semidirect |
| 5. #22549778 | C2 | semidirect |
| 6. #22549777 | C2 | semidirect |
| 7. #22549754 | C2 | semidirect |
| 8. #22549735 | C2 | semidirect |
| 9. #391×C127 | C2 | semidirect |
| 12. C2×#14523249 | C4 | semidirect |
| 40. C2×D508 | C2×C4 | semidirect |
| 49. C2×C4×D127 | C2×C4 | semidirect |
| 61. C2×Q8×C127 | C2×C4 | semidirect |
| 90. C4×D127 | C22⋊C4 | semidirect |
| 134. C127 | #2311 | semidirect |
| 139. #391 | D127 | semidirect |
| 171. C2×Q8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523249 | 2 |
| C2×#16861166 | 2 |
| C2×C4⋊C4×D127 | 2 |
| #22549783 | 2 |
| #22549778 | 2 |
| #22549777 | 2 |
| #22549754 | 2 |
| #22549735 | 2 |
| #391×C127 | 2 |
| #2311 | 127 |