Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. C22×Dic508 | C2 | semidirect |
| 2. #22550316 | C2 | direct (N × H) |
| 3. C2×#16861155 | C2 | semidirect |
| 4. C2×#16861153 | C2 | semidirect |
| 5. C2×#16861149 | C2 | semidirect |
| 11. C2×Dic508 | C22 | semidirect |
| 12. #16861155 | C22 | semidirect |
| 13. #16861153 | C22 | semidirect |
| 14. #16861149 | C22 | semidirect |
| 81. C2×C127 | #510 | semidirect |
| 84. C127 | C2×#510 | semidirect |
| 165. C2 | #22550316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic508 | 2 |
| #22550316 | 2 |
| C2×#16861155 | 2 |
| C2×#16861153 | 2 |
| C2×#16861149 | 2 |
| C2×#135×C127 | 2 |
| C2×#510 | 127 |