Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 3. #30656625 | C2 | semidirect |
| 4. #30656625 | C2 | semidirect |
| 5. #30656624 | C2 | semidirect |
| 6. #30656588 | C2 | semidirect |
| 7. C22⋊C4×Dic257 | C2 | semidirect |
| 8. C4×C22⋊Dic257 | C2 | semidirect |
| 11. #22551573 | C4 | semidirect |
| 34. C22×Dic257 | C2×C4 | semidirect |
| 41. #16861597 | C2×C4 | semidirect |
| 45. C22⋊Dic257 | C2×C4 | semidirect |
| 126. C257 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551573 | 2 |
| #30656640 | 2 |
| #30656625 | 2 |
| #30656624 | 2 |
| #30656588 | 2 |
| C22⋊C4×Dic257 | 2 |
| C4×C22⋊Dic257 | 2 |
| #386×C257 | 2 |
| #2374 | 257 |