Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#16861228 | C2 | semidirect |
| 2. C2×D8×D127 | C2 | semidirect |
| 3. #22550310 | C2 | direct (N × H) |
| 4. C2×#16861154 | C2 | semidirect |
| 5. C2×#16861153 | C2 | semidirect |
| 6. C2×#16861150 | C2 | semidirect |
| 7. C2×#16861148 | C2 | semidirect |
| 8. C2×D16×C127 | C2 | semidirect |
| 12. #16861228 | C22 | semidirect |
| 13. C2×Dic508 | C22 | semidirect |
| 18. D8×D127 | C22 | semidirect |
| 20. #16861154 | C22 | semidirect |
| 21. #16861153 | C22 | semidirect |
| 22. #16861150 | C22 | semidirect |
| 23. #16861148 | C22 | semidirect |
| 24. C2×C127⋊C16 | C22 | semidirect |
| 26. C2×D8×C127 | C22 | semidirect |
| 27. D16×C127 | C22 | semidirect |
| 28. C2×C16×C127 | C22 | semidirect |
| 41. Dic508 | C23 | semidirect |
| 49. C127⋊C16 | C23 | semidirect |
| 55. D8×C127 | C23 | semidirect |
| 57. C16×C127 | C23 | semidirect |
| 99. C2×C127 | #509 | semidirect |
| 104. C127 | C2×#509 | semidirect |
| 111. C2×D16 | D127 | semidirect |
| 124. C2×D8 | C2×D127 | semidirect |
| 129. D16 | C2×D127 | semidirect |
| 132. C2×C16 | C2×D127 | semidirect |
| 155. D8 | C22×D127 | semidirect |
| 161. C16 | C22×D127 | semidirect |
| 205. C2 | #22550310 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861228 | 2 |
| C2×D8×D127 | 2 |
| #22550310 | 2 |
| C2×#16861154 | 2 |
| C2×#16861153 | 2 |
| C2×#16861150 | 2 |
| C2×#16861148 | 2 |
| C2×D16×C127 | 2 |
| C2×#509 | 127 |