Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D251 | C2 | semidirect |
| 3. C2×#22548631 | C2 | semidirect |
| 4. C2×#22548631 | C2 | semidirect |
| 5. #30631650 | C2 | semidirect |
| 6. #30631456 | C2 | semidirect |
| 7. #343×C251 | C2 | semidirect |
| 52. #16860794 | D4 | semidirect |
| 64. M16×C251 | D4 | semidirect |
| 128. C2×D251 | #100 | semidirect |
| 144. C251 | #1900 | semidirect |
| 152. #343 | D251 | semidirect |
| 204. M16 | D1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D251 | 2 |
| C2×#22548690 | 2 |
| C2×#22548631 | 2 |
| #30631650 | 2 |
| #30631456 | 2 |
| #343×C251 | 2 |
| #1900 | 251 |