Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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×C8×Dic127 | C2 | semidirect |
| 4. #22549630 | C2 | semidirect |
| 9. C22⋊(C127⋊C8) | C4 | semidirect |
| 14. C22×C8×C127 | C4 | semidirect |
| 21. C22⋊Dic127 | C8 | direct (N × H) |
| 38. C2×Dic127 | C2×C8 | semidirect |
| 55. C8×C127 | C22⋊C4 | semidirect |
| 59. C22×C127 | C4×C8 | semidirect |
| 75. C127 | C8×C22⋊C4 | semidirect |
| 84. C22×C8 | Dic127 | semidirect |
| 130. C8 | C22⋊Dic127 | direct (N × H) |
| 134. C22 | C8×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C127⋊C8) | 2 |
| C2×C8×Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549630 | 2 |
| C23×C8×C127 | 2 |
| C8×C22⋊C4 | 127 |