Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
908 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C4⋊Dic127 | C2 | semidirect |
| 3. #22549813 | C2 | direct (N × H) |
| 4. C2×#95×C127 | C2 | semidirect |
| 8. C2×C4⋊Dic127 | C22 | semidirect |
| 12. #95×C127 | C22 | semidirect |
| 54. C2×C127 | #399 | semidirect |
| 60. C127 | C2×#399 | semidirect |
| 64. C2×#95 | D127 | semidirect |
| 72. #95 | C2×D127 | semidirect |
| 115. C2 | #22549813 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic127 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| #22549813 | 2 |
| C2×#95×C127 | 2 |
| C2×#399 | 127 |