Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
150 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 56. C8×C257 | Q16 | semidirect |
| 70. C257 | #1672 | semidirect |
| 127. C8 | #16861608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657135 | 2 |
| #30657032 | 2 |
| #30656947 | 2 |
| #30656488 | 2 |
| #30656485 | 2 |
| #30656482 | 2 |
| C8×Q8×C257 | 2 |
| #1672 | 257 |