Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22550426 | C2 | semidirect |
| 3. #22550271 | C2 | semidirect |
| 4. #22550268 | C2 | semidirect |
| 5. #22550266 | C2 | semidirect |
| 6. #22550263 | C2 | semidirect |
| 7. C2×#16861120 | C2 | semidirect |
| 8. #532×C127 | C2 | semidirect |
| 40. C2×C127⋊C8 | D4 | semidirect |
| 98. C127 | #3150 | semidirect |
| 101. #532 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861229 | 2 |
| #22550426 | 2 |
| #22550271 | 2 |
| #22550268 | 2 |
| #22550266 | 2 |
| #22550263 | 2 |
| C2×#16861120 | 2 |
| #532×C127 | 2 |
| #3150 | 127 |