Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×#16861171 | C2 | semidirect |
| 3. #22549987 | C2 | direct (N × H) |
| 4. C2×#16861129 | C2 | semidirect |
| 5. C2×#16861119 | C2 | semidirect |
| 6. C2×#106×C127 | C2 | semidirect |
| 9. C2×D1016 | C4 | semidirect |
| 13. #16861171 | C22 | semidirect |
| 16. #16861129 | C22 | semidirect |
| 17. #16861119 | C22 | semidirect |
| 20. #106×C127 | C22 | semidirect |
| 24. C2×D508 | C2×C4 | semidirect |
| 29. D1016 | C2×C4 | semidirect |
| 37. C2×C8×C127 | C2×C4 | semidirect |
| 47. D508 | C22×C4 | semidirect |
| 59. C8×C127 | C22×C4 | semidirect |
| 72. C2×C127 | #442 | semidirect |
| 77. C127 | C2×#442 | semidirect |
| 81. C2×#106 | D127 | semidirect |
| 95. #106 | C2×D127 | semidirect |
| 111. C2×C8 | C4×D127 | semidirect |
| 136. C8 | C2×C4×D127 | semidirect |
| 150. C2 | #22549987 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1016 | 2 |
| C2×#16861171 | 2 |
| #22549987 | 2 |
| C2×#16861129 | 2 |
| C2×#16861119 | 2 |
| C2×#106×C127 | 2 |
| C2×#442 | 127 |