Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1168 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 229 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×C22⋊Dic127 | C2 | semidirect |
| 2. C2×C127⋊#95 | C2 | semidirect |
| 11. C22×D4×C127 | C4 | semidirect |
| 17. C22×Dic127 | D4 | semidirect |
| 50. C23×C127 | C22⋊C4 | semidirect |
| 59. C2×C4×C127 | C22⋊C4 | semidirect |
| 85. C127 | #1438 | semidirect |
| 92. C22×D4 | Dic127 | semidirect |
| 130. C23 | C22⋊Dic127 | semidirect |
| 144. C2×C4 | C22⋊Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic127 | 2 |
| C2×C127⋊#95 | 2 |
| C23×D4×C127 | 2 |
| #1438 | 127 |