Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22550433 | C2 | semidirect |
| 3. #22550212 | C2 | semidirect |
| 4. #22550157 | C2 | semidirect |
| 5. #22550082 | C2 | semidirect |
| 7. #22549978 | C2 | semidirect |
| 8. #432×C127 | C2 | semidirect |
| 12. #16861209 | C22 | semidirect |
| 13. #16861209 | C22 | semidirect |
| 18. C4×Dic254 | C22 | semidirect |
| 26. #16861143 | C22 | semidirect |
| 27. #16861134 | C22 | semidirect |
| 30. C4⋊C8×C127 | C22 | semidirect |
| 32. #97×C127 | C22 | semidirect |
| 113. C127 | #3110 | semidirect |
| 121. #432 | D127 | semidirect |
| 141. C4⋊C8 | C2×D127 | semidirect |
| 145. #97 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550433 | 2 |
| C2×C4×D508 | 2 |
| #22550212 | 2 |
| #22550157 | 2 |
| #22550082 | 2 |
| #22550029 | 2 |
| #22549978 | 2 |
| #432×C127 | 2 |
| #3110 | 127 |