Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. C2×#16861216 | C2 | semidirect |
| 3. #22549880 | C2 | semidirect |
| 4. #22549875 | C2 | semidirect |
| 5. #22549870 | C2 | semidirect |
| 6. C2×#16861129 | C2 | semidirect |
| 7. #520×C127 | C2 | semidirect |
| 9. #16861255 | C4 | semidirect |
| 15. C2×#14523232 | C22 | semidirect |
| 16. C22×C127⋊C8 | C22 | semidirect |
| 17. #16861132 | C22 | semidirect |
| 18. #16861132 | C22 | semidirect |
| 19. #16861129 | C22 | semidirect |
| 20. #16861129 | C22 | semidirect |
| 21. #16861129 | C22 | semidirect |
| 25. #117×C127 | C22 | semidirect |
| 26. C2×C4⋊C4×C127 | C22 | semidirect |
| 30. #14523248 | C2×C4 | semidirect |
| 34. C2×D508 | C2×C4 | semidirect |
| 98. C127 | #2897 | semidirect |
| 101. #520 | D127 | semidirect |
| 118. #117 | C2×D127 | semidirect |
| 119. C2×C4⋊C4 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861255 | 2 |
| C2×#16861216 | 2 |
| #22549880 | 2 |
| #22549875 | 2 |
| #22549870 | 2 |
| C2×#16861129 | 2 |
| #520×C127 | 2 |
| #2897 | 127 |