Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. #30656765 | C2 | semidirect |
| 5. #30656498 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 7. C2×#108×C257 | C2 | semidirect |
| 19. #22551517 | C4 | semidirect |
| 20. #22551517 | C4 | semidirect |
| 21. #22551514 | C4 | semidirect |
| 22. #22551514 | C4 | semidirect |
| 109. C257 | #1866 | semidirect |
| 112. C2×#108 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551600 | 2 |
| #30656765 | 2 |
| C2×#22551518 | 2 |
| #30656734 | 2 |
| #30656498 | 2 |
| #30656491 | 2 |
| C2×#108×C257 | 2 |
| #1866 | 257 |