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. C22×#14523235 | C2 | semidirect |
| 3. C2×#16861198 | C2 | semidirect |
| 4. C2×#16861171 | C2 | semidirect |
| 5. #22550094 | C2 | direct (N × H) |
| 6. C2×Dic127⋊C8 | C2 | semidirect |
| 7. C2×#16861129 | C2 | semidirect |
| 8. C2×#103×C127 | C2 | semidirect |
| 13. C2×#14523235 | C22 | semidirect |
| 18. #16861198 | C22 | semidirect |
| 20. #16861171 | C22 | semidirect |
| 25. Dic127⋊C8 | C22 | semidirect |
| 26. #16861129 | C22 | semidirect |
| 30. #103×C127 | C22 | semidirect |
| 117. C2×C127 | #463 | semidirect |
| 124. C127 | C2×#463 | semidirect |
| 131. C2×#103 | D127 | semidirect |
| 153. #103 | C2×D127 | semidirect |
| 243. C2 | #22550094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523235 | 2 |
| C22×D1016 | 2 |
| C2×#16861198 | 2 |
| C2×#16861171 | 2 |
| #22550094 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861129 | 2 |
| C2×#103×C127 | 2 |
| C2×#463 | 127 |