Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
624 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 269 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. #30656604 | C2 | direct (N × H) |
| 10. C2×C4×Dic257 | C4 | semidirect |
| 29. C4×Dic257 | C2×C4 | semidirect |
| 77. C2×C257 | #383 | semidirect |
| 83. C257 | C2×#383 | semidirect |
| 161. C2 | #30656604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic257 | 2 |
| #30656604 | 2 |
| C2×#22551499 | 2 |
| C2×#95×C257 | 2 |
| C2×#383 | 257 |