Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
438 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 107 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×D4×Dic257 | C2 | semidirect |
| 3. C2×#22551514 | C2 | semidirect |
| 4. #30656638 | C2 | semidirect |
| 5. #30656499 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 7. C2×#102×C257 | C2 | semidirect |
| 12. C2×#16861603 | C4 | semidirect |
| 32. C2×D1028 | C2×C4 | semidirect |
| 42. C2×#14523339 | C2×C4 | semidirect |
| 84. C2×Dic257 | D8 | semidirect |
| 97. D4×C257 | C22⋊C4 | semidirect |
| 146. C257 | #1879 | semidirect |
| 151. C2×#102 | D257 | semidirect |
| 233. D4 | #16861595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861603 | 2 |
| C2×D4×Dic257 | 2 |
| C2×#22551514 | 2 |
| #30656638 | 2 |
| #30656499 | 2 |
| #30656491 | 2 |
| C2×#102×C257 | 2 |
| #1879 | 257 |