Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
608 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 237 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. #22549988 | C2 | direct (N × H) |
| 3. C2×#16861141 | C2 | semidirect |
| 4. C2×#16861130 | C2 | semidirect |
| 5. C2×#16861119 | C2 | semidirect |
| 10. D4×Dic127 | C22 | semidirect |
| 14. #16861141 | C22 | semidirect |
| 15. #16861130 | C22 | semidirect |
| 16. #16861119 | C22 | semidirect |
| 18. C2×D8×C127 | C4 | semidirect |
| 35. C2×D4×C127 | C2×C4 | semidirect |
| 38. D8×C127 | C2×C4 | semidirect |
| 39. C2×C8×C127 | C2×C4 | semidirect |
| 54. D4×C127 | C22×C4 | semidirect |
| 59. C8×C127 | C22×C4 | semidirect |
| 73. C2×C127 | #442 | semidirect |
| 77. C127 | C2×#442 | semidirect |
| 86. C2×D8 | Dic127 | semidirect |
| 101. C2×D4 | C2×Dic127 | semidirect |
| 108. D8 | C2×Dic127 | semidirect |
| 111. C2×C8 | C2×Dic127 | semidirect |
| 125. D4 | C22×Dic127 | semidirect |
| 136. C8 | C22×Dic127 | semidirect |
| 150. C2 | #22549988 | 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 |
| #22549988 | 2 |
| C2×#16861141 | 2 |
| C2×#16861130 | 2 |
| C2×#16861119 | 2 |
| C22×D8×C127 | 2 |
| C2×#442 | 127 |