Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 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. #30656868 | C2 | semidirect |
| 4. #30656487 | C2 | semidirect |
| 6. C8×#14523339 | C2 | semidirect |
| 7. Q8⋊C8×C257 | C2 | semidirect |
| 50. #14523339 | M16 | semidirect |
| 51. #14523339 | SD16 | semidirect |
| 77. C257 | #1590 | semidirect |
| 83. Q8⋊C8 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656868 | 2 |
| C4×#16861605 | 2 |
| #30656814 | 2 |
| #30656487 | 2 |
| #30656466 | 2 |
| C8×#14523339 | 2 |
| Q8⋊C8×C257 | 2 |
| #1590 | 257 |