Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1880 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 1157 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×#16861168 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic127 | C2 | semidirect |
| 4. C22×C4×Dic127 | C2 | semidirect |
| 7. #16861168 | C22 | direct (N × H) |
| 8. C2×C4⋊Dic127 | C22 | semidirect |
| 10. C2×C4×Dic127 | C22 | semidirect |
| 12. C23×C4×C127 | C4 | semidirect |
| 18. C4⋊Dic127 | C23 | semidirect |
| 20. C4×Dic127 | C23 | semidirect |
| 27. C22×C4×C127 | C2×C4 | semidirect |
| 42. C2×C4×C127 | C22×C4 | semidirect |
| 47. C22×C127 | #117 | semidirect |
| 56. C2×C127 | C2×#117 | semidirect |
| 60. C127 | C22×#117 | semidirect |
| 68. C23×C4 | Dic127 | semidirect |
| 84. C22×C4 | C2×Dic127 | semidirect |
| 102. C2×C4 | C22×Dic127 | semidirect |
| 107. C22 | #16861168 | direct (N × H) |
| 116. C2 | C2×#16861168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861168 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×C22⋊Dic127 | 2 |
| C22×C4×Dic127 | 2 |
| C24×C4×C127 | 2 |
| C22×#117 | 127 |