Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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×D8×D257 | C2 | semidirect |
| 2. C2×D4112 | C2 | semidirect |
| 3. C2×#22551533 | C2 | semidirect |
| 4. #30656974 | C2 | semidirect |
| 5. #30656537 | C2 | semidirect |
| 6. #30656516 | C2 | semidirect |
| 7. #357×C257 | C2 | semidirect |
| 10. C2×D2056 | C22 | semidirect |
| 18. C2×#16861593 | C22 | semidirect |
| 21. C2×C16×C257 | C22 | semidirect |
| 22. #107×C257 | C22 | semidirect |
| 34. D2056 | D4 | semidirect |
| 43. D8×C257 | D4 | semidirect |
| 83. C2×D257 | D16 | semidirect |
| 95. C257 | #2184 | semidirect |
| 102. #357 | D257 | semidirect |
| 116. C2×C16 | C2×D257 | semidirect |
| 117. #107 | C2×D257 | semidirect |
| 134. D8 | D1028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D257 | 2 |
| C2×D4112 | 2 |
| C2×#22551533 | 2 |
| #30656974 | 2 |
| #30656537 | 2 |
| #30656516 | 2 |
| #357×C257 | 2 |
| #2184 | 257 |