Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#16861231 | C2 | semidirect |
| 2. #22550547 | C2 | semidirect |
| 3. #22550253 | C2 | semidirect |
| 4. #22550112 | C2 | semidirect |
| 5. #22550077 | C2 | semidirect |
| 6. #22550023 | C2 | semidirect |
| 7. C4×Dic508 | C2 | semidirect |
| 8. C8×D4×C127 | C2 | semidirect |
| 38. Dic508 | D4 | semidirect |
| 87. C4×C127 | #135 | semidirect |
| 98. C127 | #3287 | semidirect |
| 106. C8×D4 | D127 | semidirect |
| 187. C4 | #16861231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| #22550547 | 2 |
| #22550253 | 2 |
| #22550112 | 2 |
| #22550077 | 2 |
| #22550023 | 2 |
| C4×Dic508 | 2 |
| C8×D4×C127 | 2 |
| #3287 | 127 |