Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#16861608 | C2 | semidirect |
| 4. C2×#22551517 | C2 | semidirect |
| 6. #30656499 | C2 | semidirect |
| 7. C2×#103×C257 | C2 | semidirect |
| 75. C22×D257 | Q16 | semidirect |
| 143. C257 | #2001 | semidirect |
| 149. C2×#103 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861608 | 2 |
| C2×#22551572 | 2 |
| C2×#22551568 | 2 |
| C2×#22551517 | 2 |
| C2×#22551504 | 2 |
| #30656499 | 2 |
| C2×#103×C257 | 2 |
| #2001 | 257 |