Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22550672 | C2 | semidirect |
| 2. C2×#16861228 | C2 | semidirect |
| 3. #131×D127 | C2 | semidirect |
| 4. #22550152 | C2 | semidirect |
| 5. #22550151 | C2 | semidirect |
| 6. #22550143 | C2 | semidirect |
| 7. #22550138 | C2 | semidirect |
| 8. #22550137 | C2 | semidirect |
| 9. #108×D127 | C2 | semidirect |
| 10. #22549857 | C2 | semidirect |
| 11. #472×C127 | C2 | semidirect |
| 25. C2×Dic508 | C22 | semidirect |
| 26. C2×#14523236 | C22 | semidirect |
| 37. #16861145 | C22 | semidirect |
| 38. #16861144 | C22 | semidirect |
| 39. #16861127 | C22 | semidirect |
| 40. #16861127 | C22 | semidirect |
| 41. #16861126 | C22 | semidirect |
| 43. C2×D8×C127 | C22 | semidirect |
| 45. #108×C127 | C22 | semidirect |
| 46. #100×C127 | C22 | semidirect |
| 167. C127 | #3067 | semidirect |
| 174. #472 | D127 | semidirect |
| 195. C2×D8 | C2×D127 | semidirect |
| 209. #108 | C2×D127 | semidirect |
| 213. #100 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550672 | 2 |
| C2×#16861228 | 2 |
| #131×D127 | 2 |
| #22550152 | 2 |
| #22550151 | 2 |
| #22550143 | 2 |
| #22550138 | 2 |
| #22550137 | 2 |
| #108×D127 | 2 |
| #22549857 | 2 |
| #472×C127 | 2 |
| #3067 | 127 |