Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×D4×Dic127 | C2 | semidirect |
| 3. C2×#16861171 | C2 | semidirect |
| 4. #22549985 | C2 | direct (N × H) |
| 5. C2×#16861140 | C2 | semidirect |
| 6. C2×#16861131 | C2 | semidirect |
| 7. C2×#16861119 | C2 | semidirect |
| 8. C2×#102×C127 | C2 | semidirect |
| 12. C2×#14523233 | C4 | semidirect |
| 16. D4×Dic127 | C22 | semidirect |
| 18. #16861171 | C22 | semidirect |
| 23. #16861140 | C22 | semidirect |
| 24. #16861131 | C22 | semidirect |
| 25. #16861119 | C22 | semidirect |
| 29. #102×C127 | C22 | semidirect |
| 33. C2×D508 | C2×C4 | semidirect |
| 42. #14523233 | C2×C4 | semidirect |
| 43. C2×C127⋊C8 | C2×C4 | semidirect |
| 54. C2×D4×C127 | C2×C4 | semidirect |
| 68. D508 | C22×C4 | semidirect |
| 77. C127⋊C8 | C22×C4 | semidirect |
| 85. D4×C127 | C22×C4 | semidirect |
| 113. C2×C127 | #442 | semidirect |
| 119. C127 | C2×#442 | semidirect |
| 126. C2×#102 | D127 | semidirect |
| 147. #102 | C2×D127 | semidirect |
| 157. C2×D4 | C4×D127 | semidirect |
| 195. D4 | C2×C4×D127 | semidirect |
| 233. C2 | #22549985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523233 | 2 |
| C2×D4×Dic127 | 2 |
| C2×#16861171 | 2 |
| #22549985 | 2 |
| C2×#16861140 | 2 |
| C2×#16861131 | 2 |
| C2×#16861119 | 2 |
| C2×#102×C127 | 2 |
| C2×#442 | 127 |