Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #30631735 | C2 | semidirect |
| 5. #30631459 | C2 | semidirect |
| 6. #30631447 | C2 | semidirect |
| 7. C4×M16×C251 | C2 | semidirect |
| 16. #22548633 | C4 | semidirect |
| 17. #22548631 | C4 | semidirect |
| 95. C251 | #1932 | semidirect |
| 101. C4×M16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631735 | 2 |
| #30631703 | 2 |
| C2×#22548643 | 2 |
| #30631669 | 2 |
| #30631459 | 2 |
| #30631447 | 2 |
| C4×M16×C251 | 2 |
| #1932 | 251 |