Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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×#22551518 | C2 | semidirect |
| 3. #30656705 | C2 | semidirect |
| 4. C2×#22551502 | C2 | semidirect |
| 5. C2×#108×C257 | C2 | semidirect |
| 9. C2×Dic1028 | C4 | semidirect |
| 10. C2×#16861607 | C4 | semidirect |
| 11. C2×D2056 | C4 | semidirect |
| 85. C257 | #1975 | semidirect |
| 88. C2×#108 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551614 | 2 |
| C2×#22551518 | 2 |
| #30656705 | 2 |
| C2×#22551502 | 2 |
| C2×#108×C257 | 2 |
| #1975 | 257 |