Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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×#22551515 | C2 | semidirect |
| 4. #30656643 | C2 | semidirect |
| 5. #30656499 | C2 | semidirect |
| 6. #30656492 | C2 | semidirect |
| 11. C2×#16861606 | C4 | semidirect |
| 31. C2×Dic514 | C2×C4 | semidirect |
| 40. C2×#14523339 | C2×C4 | semidirect |
| 95. C2×C4×C257 | SD16 | semidirect |
| 133. C257 | #1877 | semidirect |
| 227. C2×C4 | #16861606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861606 | 2 |
| C2×#22551515 | 2 |
| C2×#22551513 | 2 |
| #30656643 | 2 |
| #30656499 | 2 |
| #30656492 | 2 |
| C2×C4×D4×C257 | 2 |
| #1877 | 257 |