Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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. C4×C4⋊Dic127 | C2 | semidirect |
| 3. #22549611 | C2 | semidirect |
| 4. #431×C127 | C2 | semidirect |
| 6. #16861209 | C4 | semidirect |
| 7. #16861206 | C4 | semidirect |
| 12. C4×D508 | C4 | semidirect |
| 90. C127 | #1502 | semidirect |
| 92. #431 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550426 | 2 |
| C4×C4⋊Dic127 | 2 |
| #22549611 | 2 |
| #431×C127 | 2 |
| #1502 | 127 |