Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#22551550 | C2 | semidirect |
| 3. C2×#22551514 | C2 | semidirect |
| 4. C2×#22551512 | C2 | semidirect |
| 5. C2×#22551504 | C2 | semidirect |
| 6. #30656499 | C2 | semidirect |
| 7. #340×C257 | C2 | semidirect |
| 13. #22551567 | C4 | semidirect |
| 49. C4⋊Dic257 | D4 | semidirect |
| 62. C4⋊C4×C257 | D4 | semidirect |
| 145. C257 | #1875 | semidirect |
| 153. #340 | D257 | semidirect |
| 205. C4⋊C4 | D1028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551567 | 2 |
| C2×#22551550 | 2 |
| C2×#22551514 | 2 |
| C2×#22551512 | 2 |
| C2×#22551504 | 2 |
| #30656499 | 2 |
| #340×C257 | 2 |
| #1875 | 257 |