Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
616 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 245 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×D4×Dic127 | C2 | semidirect |
| 2. D8×Dic127 | C2 | direct (N × H) |
| 3. C2×#16861143 | C2 | semidirect |
| 4. C2×#16861130 | C2 | semidirect |
| 5. C2×C8×Dic127 | C2 | semidirect |
| 10. D4×Dic127 | C22 | semidirect |
| 14. #16861143 | C22 | semidirect |
| 15. #16861130 | C22 | semidirect |
| 16. C8×Dic127 | C22 | semidirect |
| 18. C2×D8×C127 | C4 | semidirect |
| 36. C2×D4×C127 | C2×C4 | semidirect |
| 39. D8×C127 | C2×C4 | semidirect |
| 40. C2×C8×C127 | C2×C4 | semidirect |
| 46. C2×Dic127 | D8 | direct (N × H) |
| 57. D4×C127 | C22×C4 | semidirect |
| 62. C8×C127 | C22×C4 | semidirect |
| 76. Dic127 | C2×D8 | direct (N × H) |
| 78. C2×C127 | C4×D8 | semidirect |
| 83. C127 | C2×C4×D8 | semidirect |
| 92. C2×D8 | Dic127 | direct (N × H) |
| 107. C2×D4 | C2×Dic127 | semidirect |
| 115. D8 | C2×Dic127 | direct (N × H) |
| 118. C2×C8 | C2×Dic127 | semidirect |
| 132. D4 | C22×Dic127 | semidirect |
| 145. C8 | C22×Dic127 | semidirect |
| 161. C2 | D8×Dic127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic127 | 2 |
| D8×Dic127 | 2 |
| C2×#16861143 | 2 |
| C2×#16861130 | 2 |
| C2×C8×Dic127 | 2 |
| C22×D8×C127 | 2 |
| C2×C4×D8 | 127 |