Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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. #30657551 | C2 | semidirect |
| 2. C2×#22551536 | C2 | semidirect |
| 3. #30657004 | C2 | semidirect |
| 4. #30656554 | C2 | semidirect |
| 5. #30656544 | C2 | semidirect |
| 6. #30656522 | C2 | semidirect |
| 7. #509×C257 | C2 | semidirect |
| 90. C257 | #2193 | semidirect |
| 93. #509 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657551 | 2 |
| C2×#22551536 | 2 |
| #30657004 | 2 |
| #30656554 | 2 |
| #30656544 | 2 |
| #30656522 | 2 |
| #509×C257 | 2 |
| #2193 | 257 |