Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1168 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 209 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. C22×(C2×D127)⋊C4 | C2 | semidirect |
| 3. C2×C127⋊#95 | C2 | semidirect |
| 4. C2×#95×C127 | C2 | semidirect |
| 9. C22×D508 | C4 | semidirect |
| 35. C22×Dic127 | D4 | semidirect |
| 46. C22×C4×C127 | D4 | semidirect |
| 67. C22×D127 | C22⋊C4 | semidirect |
| 90. C2×C4×C127 | C22⋊C4 | semidirect |
| 129. C127 | #1438 | semidirect |
| 133. C2×#95 | D127 | semidirect |
| 174. C22×C4 | D508 | semidirect |
| 219. C2×C4 | (C2×D127)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D508 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| C2×C127⋊#95 | 2 |
| C2×#95×C127 | 2 |
| #1438 | 127 |