Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
390 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22551508 | C2 | semidirect |
| 3. #30656701 | C2 | semidirect |
| 4. #30656505 | C2 | semidirect |
| 5. C22×M16×C257 | C2 | semidirect |
| 50. M16×C257 | D4 | semidirect |
| 93. C22×C257 | #100 | semidirect |
| 113. C257 | #1900 | semidirect |
| 115. C22×M16 | D257 | semidirect |
| 159. M16 | C22⋊D257 | semidirect |
| 211. C22 | #22551508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551566 | 2 |
| C2×#22551508 | 2 |
| #30656701 | 2 |
| #30656505 | 2 |
| C22×M16×C257 | 2 |
| #1900 | 257 |