Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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×#22548698 | C2 | semidirect |
| 3. #30631589 | C2 | semidirect |
| 4. #30631585 | C2 | semidirect |
| 5. #30631578 | C2 | semidirect |
| 6. #30631566 | C2 | semidirect |
| 7. #30631547 | C2 | semidirect |
| 8. C22×C42×C251 | C2 | semidirect |
| 50. C22×C4×C251 | D4 | semidirect |
| 107. C4×C251 | #123 | semidirect |
| 117. C251 | #2854 | semidirect |
| 121. C22×C42 | D251 | semidirect |
| 161. C22×C4 | D1004 | semidirect |
| 227. C4 | #22548698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548698 | 2 |
| C2×#22548689 | 2 |
| #30631589 | 2 |
| #30631585 | 2 |
| #30631578 | 2 |
| #30631566 | 2 |
| #30631547 | 2 |
| C22×C42×C251 | 2 |
| #2854 | 251 |