Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30657466 | C2 | semidirect |
| 4. #30656482 | C2 | semidirect |
| 5. Q8⋊#14523339 | C2 | semidirect |
| 6. #30656467 | C2 | semidirect |
| 60. Q8×C257 | SD16 | semidirect |
| 90. C257 | #1626 | semidirect |
| 146. Q8 | #16861606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657466 | 2 |
| #30657083 | 2 |
| #30656934 | 2 |
| #30656482 | 2 |
| Q8⋊#14523339 | 2 |
| #30656467 | 2 |
| #460×C257 | 2 |
| #1626 | 257 |