Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
186 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 12. #22551525 | C4 | semidirect |
| 13. #22551525 | C4 | semidirect |
| 14. #22551523 | C4 | semidirect |
| 15. #22551523 | C4 | semidirect |
| 88. C257 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656773 | 2 |
| #30656765 | 2 |
| #30656693 | 2 |
| #30656501 | 2 |
| #30656497 | 2 |
| #30656492 | 2 |
| #339×C257 | 2 |
| #1922 | 257 |