Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #22549919 | C2 | semidirect |
| 4. #22549917 | C2 | semidirect |
| 5. #22549911 | C2 | semidirect |
| 6. C2×#16861141 | C2 | semidirect |
| 7. #106×D127 | C2 | semidirect |
| 8. #427×C127 | C2 | semidirect |
| 10. #16861215 | C4 | semidirect |
| 37. #14523232 | C2×C4 | semidirect |
| 38. #14523231 | C2×C4 | semidirect |
| 40. C8×D127 | C2×C4 | semidirect |
| 47. C2×C8×C127 | C2×C4 | semidirect |
| 91. C127 | #2912 | semidirect |
| 97. #427 | D127 | semidirect |
| 133. C2×C8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861215 | 2 |
| #22550356 | 2 |
| #22549919 | 2 |
| #22549917 | 2 |
| #22549911 | 2 |
| C2×#16861141 | 2 |
| #106×D127 | 2 |
| #427×C127 | 2 |
| #2912 | 127 |