Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #22550353 | C2 | semidirect |
| 4. #22549975 | C2 | semidirect |
| 5. #22549963 | C2 | semidirect |
| 6. #22549884 | C2 | semidirect |
| 8. #22549831 | C2 | semidirect |
| 9. #427×C127 | C2 | semidirect |
| 12. C2×#14523237 | C4 | semidirect |
| 17. #16861174 | C22 | semidirect |
| 23. #16861132 | C22 | semidirect |
| 25. #16861119 | C22 | semidirect |
| 26. C8×Dic127 | C22 | semidirect |
| 30. #107×C127 | C22 | semidirect |
| 31. #106×C127 | C22 | semidirect |
| 35. C2×Dic254 | C2×C4 | semidirect |
| 43. #14523237 | C2×C4 | semidirect |
| 44. #14523237 | C2×C4 | semidirect |
| 54. C2×C8×C127 | C2×C4 | semidirect |
| 104. C127 | #2949 | semidirect |
| 110. #427 | D127 | semidirect |
| 130. #107 | C2×D127 | semidirect |
| 131. #106 | C2×D127 | semidirect |
| 152. C2×C8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523237 | 2 |
| #22550353 | 2 |
| #22550350 | 2 |
| #22549975 | 2 |
| #22549963 | 2 |
| #22549884 | 2 |
| #22549880 | 2 |
| #22549831 | 2 |
| #427×C127 | 2 |
| #2949 | 127 |