Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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. #30657116 | C2 | semidirect |
| 3. #30657085 | C2 | semidirect |
| 4. #30657084 | C2 | semidirect |
| 5. #30657083 | C2 | semidirect |
| 6. C8×#14523339 | C2 | semidirect |
| 7. #486×C257 | C2 | semidirect |
| 74. C257 | #1709 | semidirect |
| 81. #486 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657116 | 2 |
| #30657113 | 2 |
| #30657085 | 2 |
| #30657084 | 2 |
| #30657083 | 2 |
| C8×#14523339 | 2 |
| #486×C257 | 2 |
| #1709 | 257 |