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 |
| 5. #30656484 | C2 | semidirect |
| 6. #30656469 | C2 | semidirect |
| 7. Q8⋊C8×C257 | C2 | semidirect |
| 64. Q8×C257 | SD16 | semidirect |
| 90. C257 | #1626 | semidirect |
| 98. Q8⋊C8 | D257 | semidirect |
| 146. Q8 | #16861607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657466 | 2 |
| #30657084 | 2 |
| #30656938 | 2 |
| #30656937 | 2 |
| #30656484 | 2 |
| #30656469 | 2 |
| Q8⋊C8×C257 | 2 |
| #1626 | 257 |