Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 2. #31823836 | C2 | semidirect |
| 3. #31823758 | C2 | semidirect |
| 4. #31823754 | C2 | semidirect |
| 5. #31823206 | C2 | semidirect |
| 6. #31823192 | C2 | semidirect |
| 7. Q8⋊C8×C281 | C2 | semidirect |
| 69. Q8×C281 | SD16 | semidirect |
| 98. C281 | #1631 | semidirect |
| 105. Q8⋊C8 | D281 | semidirect |
| 153. Q8 | #17985127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31824135 | 2 |
| #31823836 | 2 |
| #31823758 | 2 |
| #31823754 | 2 |
| #31823206 | 2 |
| #31823192 | 2 |
| Q8⋊C8×C281 | 2 |
| #1631 | 281 |