Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 57. C8×C257 | Q16 | semidirect |
| 71. C257 | #1591 | semidirect |
| 129. C8 | #16861608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656867 | 2 |
| C4×#16861608 | 2 |
| #30656489 | 2 |
| Q8⋊#14523339 | 2 |
| #30656467 | 2 |
| C8×#14523339 | 2 |
| #446×C257 | 2 |
| #1591 | 257 |