Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
656 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 3. #30656633 | C2 | semidirect |
| 5. C4×#16861597 | C2 | semidirect |
| 8. #22551551 | C4 | semidirect |
| 26. C4⋊Dic257 | C2×C4 | semidirect |
| 31. C4×Dic257 | C2×C4 | semidirect |
| 55. C2×C4×C257 | C4⋊C4 | semidirect |
| 80. C257 | #2296 | semidirect |
| 136. C2×C4 | #16861597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551551 | 2 |
| C22×C4×Dic257 | 2 |
| #30656633 | 2 |
| #30656609 | 2 |
| C4×#16861597 | 2 |
| C2×#117×C257 | 2 |
| #2296 | 257 |