Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #22550344 | C2 | semidirect |
| 3. #22549970 | C2 | semidirect |
| 4. #22549963 | C2 | semidirect |
| 5. #22549958 | C2 | semidirect |
| 6. #22549870 | C2 | semidirect |
| 7. C2×C8×Dic127 | C2 | semidirect |
| 8. #427×C127 | C2 | semidirect |
| 10. #16861231 | C4 | semidirect |
| 30. #14523248 | C2×C4 | semidirect |
| 37. Dic508 | C2×C4 | semidirect |
| 38. #14523237 | C2×C4 | semidirect |
| 39. D1016 | C2×C4 | semidirect |
| 49. C2×C8×C127 | C2×C4 | semidirect |
| 87. Dic127 | #135 | semidirect |
| 93. C127 | C4×#135 | semidirect |
| 99. #427 | D127 | semidirect |
| 136. 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×#16861231 | 2 |
| #22550344 | 2 |
| #22549970 | 2 |
| #22549963 | 2 |
| #22549958 | 2 |
| #22549870 | 2 |
| C2×C8×Dic127 | 2 |
| #427×C127 | 2 |
| C4×#135 | 127 |