Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×C4⋊#14523339 | C2 | semidirect |
| 3. C2×#22551521 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 7. #336×C257 | C2 | semidirect |
| 43. #16861595 | C8 | semidirect |
| 72. C2×Dic257 | C2×C8 | semidirect |
| 85. C2×C4×C257 | C2×C8 | semidirect |
| 107. C2×D257 | C4⋊C8 | semidirect |
| 125. C257 | #1850 | semidirect |
| 133. #336 | D257 | semidirect |
| 209. C2×C4 | C8×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D257 | 2 |
| C2×C4⋊#14523339 | 2 |
| C2×#22551521 | 2 |
| C2×#22551504 | 2 |
| C4×#16861595 | 2 |
| #30656491 | 2 |
| #336×C257 | 2 |
| #1850 | 257 |