Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
182 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 67 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. #30631766 | C2 | semidirect |
| 3. C8×D1004 | C2 | semidirect |
| 4. #30631440 | C2 | semidirect |
| 5. #30631416 | C2 | semidirect |
| 6. #30631416 | C2 | semidirect |
| 7. #322×C251 | C2 | semidirect |
| 47. D1004 | M16 | semidirect |
| 63. C8×C251 | D8 | semidirect |
| 83. C251 | #1581 | semidirect |
| 91. #322 | D251 | semidirect |
| 147. C8 | D2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D2008 | 2 |
| #30631766 | 2 |
| C8×D1004 | 2 |
| #30631440 | 2 |
| #30631416 | 2 |
| #322×C251 | 2 |
| #1581 | 251 |