Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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×#22551527 | C2 | semidirect |
| 4. #30656495 | C2 | semidirect |
| 5. #338×C257 | C2 | semidirect |
| 67. C257 | #1813 | semidirect |
| 73. #338 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551600 | 2 |
| C2×#22551527 | 2 |
| #30656719 | 2 |
| #30656495 | 2 |
| #338×C257 | 2 |
| #1813 | 257 |