Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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×#22551537 | C2 | semidirect |
| 3. #30657121 | C2 | semidirect |
| 4. C4×D2056 | C2 | semidirect |
| 5. #30656542 | C2 | semidirect |
| 6. #30656539 | C2 | semidirect |
| 7. C4⋊C16×C257 | C2 | semidirect |
| 76. C257 | #2210 | semidirect |
| 82. C4⋊C16 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551537 | 2 |
| C2×D4112 | 2 |
| #30657121 | 2 |
| C4×D2056 | 2 |
| #30656542 | 2 |
| #30656539 | 2 |
| C4⋊C16×C257 | 2 |
| #2210 | 257 |