Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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×#22548709 | C2 | semidirect |
| 2. #30631578 | C2 | semidirect |
| 3. #30631571 | C2 | semidirect |
| 5. #30631560 | C2 | semidirect |
| 6. #30631555 | C2 | semidirect |
| 7. C22×C42×C251 | C2 | semidirect |
| 40. C42×C251 | D4 | semidirect |
| 65. C22×C251 | #126 | semidirect |
| 82. C251 | #2852 | semidirect |
| 85. C22×C42 | D251 | semidirect |
| 123. C42 | C22⋊D251 | semidirect |
| 151. C22 | #22548709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548709 | 2 |
| #30631578 | 2 |
| #30631571 | 2 |
| #30631566 | 2 |
| #30631560 | 2 |
| #30631555 | 2 |
| C22×C42×C251 | 2 |
| #2852 | 251 |