Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. C2×#22548648 | C2 | semidirect |
| 4. #30631585 | C2 | semidirect |
| 5. #30631449 | C2 | semidirect |
| 6. #30631442 | C2 | semidirect |
| 15. #22548636 | C4 | semidirect |
| 31. C2×C251⋊C8 | C2×C4 | semidirect |
| 35. C4⋊Dic251 | C2×C4 | semidirect |
| 75. D4×C251 | C4⋊C4 | semidirect |
| 123. C251 | #1862 | semidirect |
| 191. D4 | Dic251⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548648 | 2 |
| C2×#22548636 | 2 |
| #30631585 | 2 |
| #30631449 | 2 |
| #30631442 | 2 |
| C2×C4×D4×C251 | 2 |
| #1862 | 251 |