Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1664 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 981 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×C4×Dic254 | C2 | direct (N × H) |
| 7. C22×Dic254 | C4 | direct (N × H) |
| 11. C4×Dic254 | C22 | direct (N × H) |
| 19. C2×Dic254 | C2×C4 | direct (N × H) |
| 31. C22×C4×C127 | Q8 | semidirect |
| 36. Dic254 | C22×C4 | direct (N × H) |
| 47. C2×C4×C127 | C2×Q8 | semidirect |
| 51. C22×C127 | C4×Q8 | semidirect |
| 58. C4×C127 | C22×Q8 | semidirect |
| 61. C2×C127 | C2×C4×Q8 | semidirect |
| 66. C127 | C22×C4×Q8 | semidirect |
| 94. C22×C4 | Dic254 | direct (N × H) |
| 113. C2×C4 | C2×Dic254 | direct (N × H) |
| 117. C22 | C4×Dic254 | direct (N × H) |
| 126. C4 | C22×Dic254 | direct (N × H) |
| 127. C2 | C2×C4×Dic254 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic254 | 2 |
| C2×C4×Dic254 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×C4×Dic127 | 2 |
| C22×C42×C127 | 2 |
| C22×C4×Q8 | 127 |