Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30656491 | C2 | semidirect |
| 25. C22⋊Dic257 | C8 | semidirect |
| 44. C2×Dic257 | C2×C8 | semidirect |
| 67. C22×C257 | C4⋊C8 | semidirect |
| 85. C257 | #1850 | semidirect |
| 153. C22 | #22551521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551521 | 2 |
| C2×C22⋊#14523339 | 2 |
| C4×C22⋊Dic257 | 2 |
| #30656491 | 2 |
| C23×C8×C257 | 2 |
| #1850 | 257 |