Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22550583 | C2 | semidirect |
| 3. #22550223 | C2 | semidirect |
| 4. #22550195 | C2 | semidirect |
| 5. #22550167 | C2 | semidirect |
| 6. #22550105 | C2 | semidirect |
| 7. #22550077 | C2 | semidirect |
| 8. #22550029 | C2 | semidirect |
| 9. C4×#14523237 | C2 | semidirect |
| 10. C2×#16861131 | C2 | semidirect |
| 11. C8×D4×C127 | C2 | semidirect |
| 15. C2×#14523237 | C22 | semidirect |
| 16. #16861209 | C22 | semidirect |
| 19. #16861188 | C22 | semidirect |
| 24. C4×Dic254 | C22 | semidirect |
| 27. C2×C4⋊Dic127 | C22 | semidirect |
| 28. #16861141 | C22 | semidirect |
| 29. #16861141 | C22 | semidirect |
| 30. #16861134 | C22 | semidirect |
| 33. #16861131 | C22 | semidirect |
| 34. #16861131 | C22 | semidirect |
| 35. #16861131 | C22 | semidirect |
| 36. C22×C8×C127 | C22 | semidirect |
| 38. C4⋊C8×C127 | C22 | semidirect |
| 39. C22⋊C8×C127 | C22 | semidirect |
| 40. C4×C8×C127 | C22 | semidirect |
| 100. D4×C127 | SD16 | semidirect |
| 137. C127 | #3295 | semidirect |
| 147. C8×D4 | D127 | semidirect |
| 153. C22×C8 | C2×D127 | semidirect |
| 169. C4⋊C8 | C2×D127 | semidirect |
| 176. C22⋊C8 | C2×D127 | semidirect |
| 177. C4×C8 | C2×D127 | semidirect |
| 231. D4 | #14523237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550583 | 2 |
| D4×D508 | 2 |
| #22550223 | 2 |
| #22550195 | 2 |
| #22550167 | 2 |
| #22550105 | 2 |
| #22550077 | 2 |
| #22550029 | 2 |
| C4×#14523237 | 2 |
| C2×#16861131 | 2 |
| C8×D4×C127 | 2 |
| #3295 | 127 |