Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30656773 | C2 | semidirect |
| 3. #30656755 | C2 | semidirect |
| 4. #30656754 | C2 | semidirect |
| 5. #30656710 | C2 | semidirect |
| 6. #30656693 | C2 | semidirect |
| 7. #410×C257 | C2 | semidirect |
| 13. C2×#16861608 | C4 | semidirect |
| 14. C2×#16861606 | C4 | semidirect |
| 15. C2×#16861605 | C4 | semidirect |
| 16. C2×#16861603 | C4 | semidirect |
| 132. C257 | #1976 | semidirect |
| 139. #410 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551612 | 2 |
| #30656773 | 2 |
| #30656755 | 2 |
| #30656754 | 2 |
| #30656710 | 2 |
| #30656693 | 2 |
| #410×C257 | 2 |
| #1976 | 257 |