Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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×Dic127⋊C8 | C2 | semidirect |
| 4. #22549630 | C2 | semidirect |
| 25. C22⋊Dic127 | C8 | semidirect |
| 44. C2×Dic127 | C2×C8 | semidirect |
| 67. C22×C127 | C4⋊C8 | semidirect |
| 86. C127 | #1850 | semidirect |
| 153. C22 | Dic127⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic127⋊C8 | 2 |
| C2×C22⋊(C127⋊C8) | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549630 | 2 |
| C23×C8×C127 | 2 |
| #1850 | 127 |