Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
512 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 309 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. #22549914 | C2 | direct (N × H) |
| 3. C2×#16861143 | C2 | semidirect |
| 4. C2×#16861141 | C2 | semidirect |
| 11. #16861143 | C22 | semidirect |
| 12. #16861141 | C22 | semidirect |
| 14. C22×C8×C127 | C4 | semidirect |
| 32. C2×C8×C127 | C2×C4 | semidirect |
| 64. C2×C127 | #427 | semidirect |
| 68. C127 | C2×#427 | semidirect |
| 75. C22×C8 | Dic127 | semidirect |
| 96. C2×C8 | C2×Dic127 | semidirect |
| 132. C2 | #22549914 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861168 | 2 |
| #22549914 | 2 |
| C2×#16861143 | 2 |
| C2×#16861141 | 2 |
| C23×C8×C127 | 2 |
| C2×#427 | 127 |