Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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. #30656628 | C2 | semidirect |
| 3. #30656626 | C2 | semidirect |
| 4. #30656595 | C2 | semidirect |
| 6. C4×C22⋊Dic257 | C2 | semidirect |
| 7. C4×C22⋊C4×C257 | C2 | semidirect |
| 10. C2×#16861597 | C22 | semidirect |
| 12. C2×#16861595 | C4 | semidirect |
| 17. C2×C4×Dic257 | C22 | semidirect |
| 18. #22551499 | C22 | semidirect |
| 19. #22551499 | C22 | semidirect |
| 22. C2×C42×C257 | C22 | semidirect |
| 23. #95×C257 | C22 | semidirect |
| 99. C257 | #2312 | semidirect |
| 107. C4×C22⋊C4 | D257 | semidirect |
| 120. C2×C42 | C2×D257 | semidirect |
| 123. #95 | C2×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861595 | 2 |
| #30656628 | 2 |
| #30656626 | 2 |
| #30656595 | 2 |
| #30656592 | 2 |
| C4×C22⋊Dic257 | 2 |
| C4×C22⋊C4×C257 | 2 |
| #2312 | 257 |