Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14523237 | C2 | semidirect |
| 2. #22550447 | C2 | semidirect |
| 4. #22550122 | C2 | semidirect |
| 5. #22550105 | C2 | semidirect |
| 6. #22549914 | C2 | semidirect |
| 7. #22549886 | C2 | semidirect |
| 8. #22549882 | C2 | semidirect |
| 9. C2×#131×C127 | C2 | semidirect |
| 20. #16861188 | C22 | semidirect |
| 25. #16861143 | C22 | semidirect |
| 26. #16861141 | C22 | semidirect |
| 27. #16861134 | C22 | semidirect |
| 32. C2×M16×C127 | C22 | semidirect |
| 34. C22×C8×C127 | C22 | semidirect |
| 67. C2×C8×C127 | D4 | semidirect |
| 121. C127 | #3057 | semidirect |
| 123. C2×#131 | D127 | semidirect |
| 139. C2×M16 | C2×D127 | semidirect |
| 141. C22×C8 | C2×D127 | semidirect |
| 179. C2×C8 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523237 | 2 |
| #22550447 | 2 |
| #22550440 | 2 |
| #22550122 | 2 |
| #22550105 | 2 |
| #22549914 | 2 |
| #22549886 | 2 |
| #22549882 | 2 |
| C2×#131×C127 | 2 |
| #3057 | 127 |