Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×D257 | C2 | semidirect |
| 3. C2×#22551519 | C2 | semidirect |
| 4. #30656700 | C2 | semidirect |
| 5. #30656498 | C2 | semidirect |
| 6. #30656497 | C2 | semidirect |
| 7. C2×#104×C257 | C2 | semidirect |
| 12. #22551568 | C4 | semidirect |
| 13. #22551563 | C4 | semidirect |
| 42. C4⋊Dic257 | C2×C4 | semidirect |
| 50. C4×Dic257 | D4 | semidirect |
| 55. C2×Q8×C257 | C2×C4 | semidirect |
| 57. C2×D4×C257 | C2×C4 | semidirect |
| 65. C42×C257 | D4 | semidirect |
| 113. C2×D257 | #104 | semidirect |
| 129. C257 | #1896 | semidirect |
| 134. C2×#104 | D257 | semidirect |
| 162. C2×Q8 | C4×D257 | semidirect |
| 165. C2×D4 | C4×D257 | semidirect |
| 195. C42 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657244 | 2 |
| C2×C42×D257 | 2 |
| C2×#22551519 | 2 |
| #30656700 | 2 |
| #30656498 | 2 |
| #30656497 | 2 |
| C2×#104×C257 | 2 |
| #1896 | 257 |