Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #30656644 | C2 | semidirect |
| 3. #30656629 | C2 | semidirect |
| 4. #30656627 | C2 | semidirect |
| 6. C4×#16861595 | C2 | semidirect |
| 7. #30656584 | C2 | semidirect |
| 8. #30656582 | C2 | semidirect |
| 9. #391×C257 | C2 | semidirect |
| 12. #22551581 | C4 | semidirect |
| 46. #16861595 | C2×C4 | semidirect |
| 47. #16861595 | C2×C4 | semidirect |
| 51. C4×Dic257 | C2×C4 | semidirect |
| 54. C2×Q8×C257 | C2×C4 | semidirect |
| 123. C257 | #2372 | semidirect |
| 127. #391 | D257 | semidirect |
| 159. C2×Q8 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551581 | 2 |
| #30656644 | 2 |
| #30656629 | 2 |
| #30656627 | 2 |
| #30656615 | 2 |
| C4×#16861595 | 2 |
| #30656584 | 2 |
| #30656582 | 2 |
| #391×C257 | 2 |
| #2372 | 257 |