Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22550676 | C2 | semidirect |
| 2. C2×#16861231 | C2 | semidirect |
| 3. C2×#16861215 | C2 | semidirect |
| 4. #22550152 | C2 | semidirect |
| 5. #22550147 | C2 | semidirect |
| 6. #22550140 | C2 | semidirect |
| 7. #22549858 | C2 | semidirect |
| 8. C2×#108×C127 | C2 | semidirect |
| 20. C2×Dic508 | C22 | semidirect |
| 21. C2×#14523237 | C22 | semidirect |
| 22. C2×D1016 | C22 | semidirect |
| 30. #16861127 | C22 | semidirect |
| 31. #16861125 | C22 | semidirect |
| 34. #108×C127 | C22 | semidirect |
| 35. #108×C127 | C22 | semidirect |
| 133. C127 | #3067 | semidirect |
| 140. C2×#108 | D127 | semidirect |
| 165. #108 | C2×D127 | semidirect |
| 166. #108 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550676 | 2 |
| C2×#16861231 | 2 |
| C2×#16861215 | 2 |
| #22550152 | 2 |
| #22550147 | 2 |
| #22550140 | 2 |
| #22549858 | 2 |
| C2×#108×C127 | 2 |
| #3067 | 127 |