Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16861200 | C2 | semidirect |
| 3. #22550239 | C2 | direct (N × H) |
| 4. C2×#16861131 | C2 | semidirect |
| 5. C2×#16861130 | C2 | semidirect |
| 6. C2×#16861129 | C2 | semidirect |
| 7. C2×#16861119 | C2 | semidirect |
| 8. C2×#102×C127 | C2 | semidirect |
| 16. #16861200 | C22 | semidirect |
| 21. #16861131 | C22 | semidirect |
| 22. #16861130 | C22 | semidirect |
| 23. #16861129 | C22 | semidirect |
| 24. #16861119 | C22 | semidirect |
| 28. #102×C127 | C22 | semidirect |
| 111. C2×C127 | #490 | semidirect |
| 117. C127 | C2×#490 | semidirect |
| 124. C2×#102 | D127 | semidirect |
| 144. #102 | C2×D127 | semidirect |
| 229. C2 | #22550239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861205 | 2 |
| C2×#16861200 | 2 |
| #22550239 | 2 |
| C2×#16861131 | 2 |
| C2×#16861130 | 2 |
| C2×#16861129 | 2 |
| C2×#16861119 | 2 |
| C2×#102×C127 | 2 |
| C2×#490 | 127 |