Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. C2×#22551622 | C2 | semidirect |
| 3. C22×#16861607 | C2 | semidirect |
| 4. C2×#22551510 | C2 | semidirect |
| 5. C2×#22551508 | C2 | semidirect |
| 6. #30656502 | C2 | semidirect |
| 7. #408×C257 | C2 | semidirect |
| 127. C257 | #2019 | semidirect |
| 134. #408 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551622 | 2 |
| C2×#22551617 | 2 |
| C22×#16861607 | 2 |
| C2×#22551510 | 2 |
| C2×#22551508 | 2 |
| #30656502 | 2 |
| #408×C257 | 2 |
| #2019 | 257 |