Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 1. C8×Dic502 | C2 | semidirect |
| 4. #30631438 | C2 | semidirect |
| 5. #30631419 | C2 | semidirect |
| 7. #322×C251 | C2 | semidirect |
| 43. Dic502 | M16 | semidirect |
| 60. C8×C251 | SD16 | semidirect |
| 77. C251 | #1583 | semidirect |
| 85. #322 | D251 | semidirect |
| 138. C8 | #16860799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic502 | 2 |
| C4×#16860799 | 2 |
| #30631766 | 2 |
| #30631438 | 2 |
| #30631419 | 2 |
| #30631416 | 2 |
| #322×C251 | 2 |
| #1583 | 251 |