Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
280 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. C2×#22551521 | C2 | semidirect |
| 4. C2×#22551503 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 7. #336×C257 | C2 | semidirect |
| 122. C257 | #1924 | semidirect |
| 130. #336 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551521 | 2 |
| C2×#22551504 | 2 |
| C2×#22551503 | 2 |
| C4×#16861595 | 2 |
| #30656491 | 2 |
| #336×C257 | 2 |
| #1924 | 257 |