Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#16861231 | C2 | semidirect |
| 2. #22550317 | C2 | semidirect |
| 3. #22550316 | C2 | semidirect |
| 4. #22550312 | C2 | semidirect |
| 5. #22550311 | C2 | semidirect |
| 6. #22550306 | C2 | semidirect |
| 7. C2×#16861149 | C2 | semidirect |
| 8. C2×#135×C127 | C2 | semidirect |
| 13. #16861231 | C22 | semidirect |
| 14. C2×Dic508 | C22 | semidirect |
| 16. C2×D1016 | C22 | semidirect |
| 17. #16861155 | C22 | semidirect |
| 18. #16861153 | C22 | semidirect |
| 19. #16861152 | C22 | semidirect |
| 20. #16861150 | C22 | semidirect |
| 21. #16861149 | C22 | semidirect |
| 22. #16861149 | C22 | semidirect |
| 23. C2×C127⋊C16 | C22 | semidirect |
| 28. #135×C127 | C22 | semidirect |
| 29. C2×Q16×C127 | C22 | semidirect |
| 31. C2×D8×C127 | C22 | semidirect |
| 121. C127 | #3414 | semidirect |
| 123. C2×#135 | D127 | semidirect |
| 139. #135 | C2×D127 | semidirect |
| 141. C2×Q16 | C2×D127 | semidirect |
| 145. C2×D8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| #22550317 | 2 |
| #22550316 | 2 |
| #22550312 | 2 |
| #22550311 | 2 |
| #22550306 | 2 |
| C2×#16861149 | 2 |
| C2×#135×C127 | 2 |
| #3414 | 127 |