Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
688 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 213 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. #30656640 | C2 | semidirect |
| 2. #30656630 | C2 | semidirect |
| 3. #30656617 | C2 | semidirect |
| 4. #30656593 | C2 | semidirect |
| 6. C23×Dic257 | C22 | semidirect |
| 7. C2×C4⋊Dic257 | C22 | semidirect |
| 10. C2×C22⋊Dic257 | C22 | semidirect |
| 11. C2×C4×Dic257 | C22 | semidirect |
| 12. #22551499 | C22 | semidirect |
| 15. #120×C257 | C4 | semidirect |
| 27. C24×C257 | C2×C4 | semidirect |
| 34. C22⋊C4×C257 | C2×C4 | semidirect |
| 76. C257 | #2375 | semidirect |
| 86. #120 | Dic257 | semidirect |
| 96. C24 | C2×Dic257 | semidirect |
| 110. C22⋊C4 | C2×Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656640 | 2 |
| #30656630 | 2 |
| #30656617 | 2 |
| #30656593 | 2 |
| C2×#120×C257 | 2 |
| #2375 | 257 |