Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 598 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×C22⋊C4×D251 | C2 | semidirect |
| 3. C2×#22548630 | C2 | semidirect |
| 4. #30631542 | C2 | semidirect |
| 5. #30631453 | C2 | semidirect |
| 6. #30631453 | C2 | semidirect |
| 7. C2×#99×C251 | C2 | semidirect |
| 9. C22×C22⋊D251 | C4 | semidirect |
| 19. C2×(C2×D251)⋊C4 | C4 | semidirect |
| 41. C22×Dic251 | C2×C4 | semidirect |
| 49. C22⋊Dic251 | D4 | semidirect |
| 54. C24×C251 | C2×C4 | semidirect |
| 64. C22×C4×C251 | C2×C4 | semidirect |
| 68. C22⋊C4×C251 | D4 | semidirect |
| 152. C2×D251 | #99 | semidirect |
| 170. C251 | #1898 | semidirect |
| 175. C2×#99 | D251 | semidirect |
| 207. C24 | C4×D251 | semidirect |
| 225. C22×C4 | C4×D251 | semidirect |
| 239. C22⋊C4 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548683 | 2 |
| C2×C22⋊C4×D251 | 2 |
| C2×#22548630 | 2 |
| #30631542 | 2 |
| #30631453 | 2 |
| C2×#99×C251 | 2 |
| #1898 | 251 |