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. #30657172 | C2 | semidirect |
| 3. C2×#22551537 | C2 | semidirect |
| 4. #30657008 | C2 | semidirect |
| 5. #30656552 | C2 | semidirect |
| 6. #30656520 | C2 | semidirect |
| 7. #359×C257 | C2 | semidirect |
| 90. C257 | #2193 | semidirect |
| 97. #359 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657551 | 2 |
| #30657172 | 2 |
| C2×#22551537 | 2 |
| #30657008 | 2 |
| #30656552 | 2 |
| #30656520 | 2 |
| #359×C257 | 2 |
| #2193 | 257 |