Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. #30656864 | C2 | semidirect |
| 4. #30656467 | C2 | semidirect |
| 6. #30656459 | C2 | semidirect |
| 7. #334×C257 | C2 | semidirect |
| 53. #14523339 | SD16 | semidirect |
| 77. C257 | #1582 | semidirect |
| 82. #334 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656864 | 2 |
| C4×#16861607 | 2 |
| #30656802 | 2 |
| #30656467 | 2 |
| #30656464 | 2 |
| #30656459 | 2 |
| #334×C257 | 2 |
| #1582 | 257 |