Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22550427 | C2 | semidirect |
| 2. C4×D4×D127 | C2 | semidirect |
| 3. #22550191 | C2 | semidirect |
| 4. #22550153 | C2 | semidirect |
| 5. #22550072 | C2 | semidirect |
| 6. #22550071 | C2 | semidirect |
| 7. #22550011 | C2 | semidirect |
| 8. #22549958 | C2 | semidirect |
| 9. #22549956 | C2 | semidirect |
| 10. #22549928 | C2 | semidirect |
| 11. #474×C127 | C2 | semidirect |
| 17. #16861206 | C22 | semidirect |
| 25. #16861171 | C22 | semidirect |
| 31. #16861142 | C22 | semidirect |
| 32. C4⋊(C127⋊C8) | C22 | semidirect |
| 33. #16861131 | C22 | semidirect |
| 35. #16861129 | C22 | semidirect |
| 37. C8×Dic127 | C22 | semidirect |
| 38. C4⋊Q8×C127 | C22 | semidirect |
| 40. #107×C127 | C22 | semidirect |
| 41. C4⋊C8×C127 | C22 | semidirect |
| 96. D508 | #41 | semidirect |
| 110. C4×D127 | D8 | semidirect |
| 115. D4×C127 | #41 | semidirect |
| 155. C127 | #3100 | semidirect |
| 160. #474 | D127 | semidirect |
| 172. C4⋊Q8 | C2×D127 | semidirect |
| 189. #107 | C2×D127 | semidirect |
| 191. C4⋊C8 | C2×D127 | semidirect |
| 256. D4 | #14523249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550427 | 2 |
| C4×D4×D127 | 2 |
| #22550191 | 2 |
| #22550153 | 2 |
| #22550072 | 2 |
| #22550071 | 2 |
| #22550011 | 2 |
| #22549958 | 2 |
| #22549956 | 2 |
| #22549928 | 2 |
| #474×C127 | 2 |
| #3100 | 127 |