Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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. M32×D257 | C2 | semidirect |
| 3. C2×C16×D257 | C2 | semidirect |
| 4. #30656522 | C2 | semidirect |
| 5. #30656521 | C2 | semidirect |
| 6. #30656520 | C2 | semidirect |
| 7. #350×C257 | C2 | semidirect |
| 18. #22551532 | C22 | semidirect |
| 20. C2×#16861593 | C22 | semidirect |
| 25. M32×C257 | C22 | semidirect |
| 26. C2×C16×C257 | C22 | semidirect |
| 107. D257 | #350 | direct (N × H) |
| 108. C257 | C2×#350 | semidirect |
| 116. #350 | D257 | direct (N × H) |
| 130. M32 | C2×D257 | semidirect |
| 135. C2×C16 | C2×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D257 | 2 |
| M32×D257 | 2 |
| C2×C16×D257 | 2 |
| #30656522 | 2 |
| #30656521 | 2 |
| #30656520 | 2 |
| #350×C257 | 2 |
| C2×#350 | 257 |