Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
| 2. #30656978 | C2 | semidirect |
| 4. #30656565 | C2 | semidirect |
| 5. #30656542 | C2 | semidirect |
| 6. #30656539 | C2 | semidirect |
| 7. C22×C16×C257 | C2 | semidirect |
| 39. C16×C257 | D4 | semidirect |
| 59. C22×C257 | SD32 | semidirect |
| 75. C257 | #2217 | semidirect |
| 78. C22×C16 | D257 | semidirect |
| 115. C16 | C22⋊D257 | semidirect |
| 138. C22 | #22551537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551537 | 2 |
| #30656978 | 2 |
| #30656973 | 2 |
| #30656565 | 2 |
| #30656542 | 2 |
| #30656539 | 2 |
| C22×C16×C257 | 2 |
| #2217 | 257 |