Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 1. C2×C4×D508 | C2 | semidirect |
| 2. #22550187 | C2 | semidirect |
| 3. #22550153 | C2 | semidirect |
| 4. #22550068 | C2 | semidirect |
| 5. #22550009 | C2 | semidirect |
| 6. C4×#14523233 | C2 | semidirect |
| 7. #22549929 | C2 | semidirect |
| 8. #532×C127 | C2 | semidirect |
| 18. #16861142 | C22 | semidirect |
| 19. C4⋊(C127⋊C8) | C22 | semidirect |
| 20. #16861130 | C22 | semidirect |
| 23. C4×C127⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C127 | C22 | semidirect |
| 26. #127×C127 | C22 | semidirect |
| 31. C4×D4×C127 | C22 | semidirect |
| 71. D508 | #41 | semidirect |
| 88. C2×C4×C127 | D8 | semidirect |
| 121. C127 | #3100 | semidirect |
| 122. #532 | D127 | semidirect |
| 134. C4⋊Q8 | C2×D127 | semidirect |
| 135. #127 | C2×D127 | semidirect |
| 144. C4×D4 | C2×D127 | semidirect |
| 208. C2×C4 | #14523233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D508 | 2 |
| #22550187 | 2 |
| #22550153 | 2 |
| #22550068 | 2 |
| #22550009 | 2 |
| C4×#14523233 | 2 |
| #22549929 | 2 |
| #532×C127 | 2 |
| #3100 | 127 |