Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 1. C22×D1016 | C2 | semidirect |
| 2. C22×#14523233 | C2 | semidirect |
| 3. C2×#16861205 | C2 | semidirect |
| 4. #22550251 | C2 | direct (N × H) |
| 5. C2×C8×Dic127 | C2 | semidirect |
| 6. C22×D8×C127 | C2 | semidirect |
| 10. C2×D1016 | C22 | semidirect |
| 12. C2×#14523233 | C22 | semidirect |
| 15. #16861205 | C22 | semidirect |
| 17. C8×Dic127 | C22 | semidirect |
| 20. C2×D8×C127 | C22 | semidirect |
| 32. C2×C127⋊C8 | D4 | semidirect |
| 43. C2×C8×C127 | D4 | semidirect |
| 52. C2×Dic127 | D8 | semidirect |
| 54. C127⋊C8 | C2×D4 | semidirect |
| 66. C8×C127 | C2×D4 | semidirect |
| 79. Dic127 | C2×D8 | semidirect |
| 81. C2×C127 | #493 | semidirect |
| 86. C127 | C2×#493 | semidirect |
| 89. C22×D8 | D127 | semidirect |
| 101. C2×D8 | C2×D127 | semidirect |
| 127. C2×C8 | C22⋊D127 | semidirect |
| 152. C8 | C2×C22⋊D127 | semidirect |
| 168. C2 | #22550251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1016 | 2 |
| C22×#14523233 | 2 |
| C2×#16861205 | 2 |
| #22550251 | 2 |
| C2×C8×Dic127 | 2 |
| C22×D8×C127 | 2 |
| C2×#493 | 127 |