Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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. #135×D127 | C2 | semidirect |
| 2. #22550318 | C2 | semidirect |
| 3. #22550315 | C2 | semidirect |
| 4. #22550313 | C2 | semidirect |
| 5. #22550310 | C2 | semidirect |
| 6. #22550308 | C2 | semidirect |
| 7. #22550306 | C2 | semidirect |
| 8. C2×#16861148 | C2 | semidirect |
| 9. #508×C127 | C2 | semidirect |
| 12. #16861231 | C22 | semidirect |
| 16. Q16×D127 | C22 | semidirect |
| 18. D8×D127 | C22 | semidirect |
| 20. Dic1016 | C22 | semidirect |
| 21. #16861155 | C22 | semidirect |
| 22. #16861154 | C22 | semidirect |
| 23. #16861153 | C22 | semidirect |
| 24. #16861152 | C22 | semidirect |
| 25. D2032 | C22 | semidirect |
| 26. #16861150 | C22 | semidirect |
| 27. #16861148 | C22 | semidirect |
| 28. #16861148 | C22 | semidirect |
| 29. C2×C127⋊C16 | C22 | semidirect |
| 30. #135×C127 | C22 | semidirect |
| 31. Q32×C127 | C22 | semidirect |
| 32. SD32×C127 | C22 | semidirect |
| 33. D16×C127 | C22 | semidirect |
| 34. C2×C16×C127 | C22 | semidirect |
| 104. C127 | #3414 | semidirect |
| 112. #508 | D127 | semidirect |
| 120. #135 | C2×D127 | semidirect |
| 127. Q32 | C2×D127 | semidirect |
| 131. SD32 | C2×D127 | semidirect |
| 134. D16 | C2×D127 | semidirect |
| 138. C2×C16 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D127 | 2 |
| #22550318 | 2 |
| #22550315 | 2 |
| #22550313 | 2 |
| #22550310 | 2 |
| #22550308 | 2 |
| #22550306 | 2 |
| C2×#16861148 | 2 |
| #508×C127 | 2 |
| #3414 | 127 |