Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
266 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 61 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×#22551533 | C2 | semidirect |
| 2. #30656973 | C2 | semidirect |
| 3. #30656538 | C2 | semidirect |
| 4. C22⋊#16861593 | C2 | semidirect |
| 5. C22×D8×C257 | C2 | semidirect |
| 6. C2×D2056 | C22 | semidirect |
| 9. C2×#16861593 | C22 | semidirect |
| 10. #22551526 | C22 | semidirect |
| 31. D8×C257 | D4 | semidirect |
| 60. C22×C257 | D16 | semidirect |
| 75. C257 | #2184 | semidirect |
| 77. C22×D8 | D257 | semidirect |
| 104. D8 | C22⋊D257 | semidirect |
| 139. C22 | #22551533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551533 | 2 |
| #30656973 | 2 |
| #30656538 | 2 |
| C22⋊#16861593 | 2 |
| C22×D8×C257 | 2 |
| #2184 | 257 |