Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. C2×#22551511 | C2 | semidirect |
| 5. #30656507 | C2 | semidirect |
| 6. #30656495 | C2 | semidirect |
| 7. #419×C257 | C2 | semidirect |
| 11. C2×#16861608 | C4 | semidirect |
| 12. C2×#16861605 | C4 | semidirect |
| 107. C257 | #1902 | semidirect |
| 112. #419 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551623 | 2 |
| #30657503 | 2 |
| #30656755 | 2 |
| C2×#22551511 | 2 |
| #30656507 | 2 |
| #30656495 | 2 |
| #419×C257 | 2 |
| #1902 | 257 |