Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 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. #22550617 | C2 | direct (N × H) |
| 2. C2×#16861206 | C2 | semidirect |
| 3. C2×#16861203 | C2 | semidirect |
| 4. C2×#16861194 | C2 | semidirect |
| 5. C2×#16861184 | C2 | semidirect |
| 6. C2×#16861182 | C2 | semidirect |
| 7. C2×#16861179 | C2 | semidirect |
| 8. C2×#126×C127 | C2 | semidirect |
| 12. C22×D508 | C22 | semidirect |
| 14. C22×C4×D127 | C22 | semidirect |
| 15. #16861206 | C22 | semidirect |
| 16. #16861203 | C22 | semidirect |
| 17. #16861194 | C22 | semidirect |
| 18. #16861184 | C22 | semidirect |
| 19. #16861182 | C22 | semidirect |
| 20. #16861179 | C22 | semidirect |
| 21. C2×Dic127⋊C4 | C22 | semidirect |
| 24. C2×(C2×D127)⋊C4 | C22 | semidirect |
| 25. #126×C127 | C22 | semidirect |
| 26. C2×C4⋊C4×C127 | C22 | semidirect |
| 28. C2×C42×C127 | C22 | semidirect |
| 39. C2×D508 | C23 | semidirect |
| 44. C2×C4×D127 | C23 | semidirect |
| 45. Dic127⋊C4 | C23 | semidirect |
| 48. (C2×D127)⋊C4 | C23 | semidirect |
| 52. C4⋊C4×C127 | C23 | semidirect |
| 54. C42×C127 | C23 | semidirect |
| 96. C2×C127 | #560 | semidirect |
| 102. C127 | C2×#560 | semidirect |
| 106. C2×#126 | D127 | semidirect |
| 119. #126 | C2×D127 | semidirect |
| 125. C2×C4⋊C4 | C2×D127 | semidirect |
| 130. C2×C42 | C2×D127 | semidirect |
| 151. C4⋊C4 | C22×D127 | semidirect |
| 156. C42 | C22×D127 | semidirect |
| 201. C2 | #22550617 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550617 | 2 |
| C2×#16861206 | 2 |
| C2×#16861203 | 2 |
| C2×#16861194 | 2 |
| C2×#16861184 | 2 |
| C2×#16861182 | 2 |
| C2×#16861179 | 2 |
| C2×#126×C127 | 2 |
| C2×#560 | 127 |