Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
402 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#22551516 | C2 | semidirect |
| 4. #30656644 | C2 | semidirect |
| 5. #30656500 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 24. C2×SD16×C257 | C4 | semidirect |
| 49. C2×Q8×C257 | C2×C4 | semidirect |
| 61. C2×C8×C257 | C2×C4 | semidirect |
| 74. C2×Dic257 | SD16 | semidirect |
| 133. C257 | #1877 | semidirect |
| 147. C2×SD16 | Dic257 | semidirect |
| 166. C2×Q8 | C2×Dic257 | semidirect |
| 188. C2×C8 | C2×Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic257 | 2 |
| C2×#22551516 | 2 |
| C2×#22551513 | 2 |
| #30656644 | 2 |
| #30656500 | 2 |
| #30656491 | 2 |
| C22×SD16×C257 | 2 |
| #1877 | 257 |