Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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. #30657178 | C2 | semidirect |
| 3. C2×#22551538 | C2 | semidirect |
| 4. #30656552 | C2 | semidirect |
| 5. #30656543 | C2 | semidirect |
| 6. #30656521 | C2 | semidirect |
| 7. #473×C257 | C2 | semidirect |
| 88. C257 | #2195 | semidirect |
| 93. #473 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657554 | 2 |
| #30657178 | 2 |
| C2×#22551538 | 2 |
| #30656552 | 2 |
| #30656543 | 2 |
| #30656521 | 2 |
| #473×C257 | 2 |
| #2195 | 257 |