Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22551527 | C2 | semidirect |
| 3. #30656741 | C2 | semidirect |
| 4. C2×#22551509 | C2 | semidirect |
| 5. C2×#22551508 | C2 | semidirect |
| 6. #30656693 | C2 | semidirect |
| 7. #418×C257 | C2 | semidirect |
| 12. C2×#16861603 | C4 | semidirect |
| 111. C257 | #1978 | semidirect |
| 116. #418 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861603 | 2 |
| C2×#22551527 | 2 |
| #30656741 | 2 |
| C2×#22551509 | 2 |
| C2×#22551508 | 2 |
| #30656693 | 2 |
| #418×C257 | 2 |
| #1978 | 257 |