Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16861233 | C2 | semidirect |
| 2. #22550424 | C2 | semidirect |
| 3. #127×D127 | C2 | semidirect |
| 4. #22550264 | C2 | semidirect |
| 5. #22550252 | C2 | semidirect |
| 6. #22550249 | C2 | semidirect |
| 7. #22550248 | C2 | semidirect |
| 8. C4×#14523231 | C2 | semidirect |
| 9. #493×C127 | C2 | semidirect |
| 14. C2×#14523237 | C22 | semidirect |
| 15. C2×#14523236 | C22 | semidirect |
| 16. C2×#14523233 | C22 | semidirect |
| 18. #16861209 | C22 | semidirect |
| 22. #16861196 | C22 | semidirect |
| 26. #16861119 | C22 | semidirect |
| 27. C4×C127⋊C8 | C22 | semidirect |
| 28. C2×D8×C127 | C22 | semidirect |
| 30. #127×C127 | C22 | semidirect |
| 31. C4×C8×C127 | C22 | semidirect |
| 48. #14523231 | D4 | semidirect |
| 77. C127⋊C8 | C2×D4 | semidirect |
| 86. C8×C127 | C2×D4 | semidirect |
| 97. C4×C127 | AGL(1,ℤ/8) | semidirect |
| 109. C127 | #3151 | semidirect |
| 115. #493 | D127 | semidirect |
| 126. C2×D8 | C2×D127 | semidirect |
| 133. #127 | C2×D127 | semidirect |
| 140. C4×C8 | C2×D127 | semidirect |
| 195. C8 | D4×D127 | semidirect |
| 209. C4 | #16861233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861233 | 2 |
| #22550424 | 2 |
| #127×D127 | 2 |
| #22550264 | 2 |
| #22550252 | 2 |
| #22550249 | 2 |
| #22550248 | 2 |
| C4×#14523231 | 2 |
| #493×C127 | 2 |
| #3151 | 127 |