Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22551526 | C2 | semidirect |
| 3. #30656539 | C2 | direct (N × H) |
| 4. C22×C16×C257 | C2 | semidirect |
| 8. C2×D2056 | C4 | semidirect |
| 12. #22551526 | C22 | semidirect |
| 15. C2×C16×C257 | C22 | semidirect |
| 24. D2056 | C2×C4 | semidirect |
| 62. C2×C257 | #357 | semidirect |
| 67. C257 | C2×#357 | semidirect |
| 70. C22×C16 | D257 | semidirect |
| 81. C2×C16 | C2×D257 | semidirect |
| 131. C2 | #30656539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2056 | 2 |
| C2×#22551526 | 2 |
| #30656539 | 2 |
| C22×C16×C257 | 2 |
| C2×#357 | 257 |