Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
220 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 89 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×#22551532 | C2 | semidirect |
| 3. #30656522 | C2 | semidirect |
| 4. C2×M32×C257 | C2 | semidirect |
| 15. C2×#16861593 | C22 | semidirect |
| 18. M32×C257 | C22 | semidirect |
| 82. C257 | #2117 | semidirect |
| 86. C2×M32 | D257 | semidirect |
| 100. M32 | C2×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551598 | 2 |
| C2×#22551532 | 2 |
| #30656522 | 2 |
| C2×M32×C257 | 2 |
| #2117 | 257 |