Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. #30631972 | C2 | semidirect |
| 4. #30631438 | C2 | semidirect |
| 5. #30631434 | C2 | semidirect |
| 7. C8×Q8×C251 | C2 | semidirect |
| 54. Q8×C251 | SD16 | semidirect |
| 62. C8×C251 | SD16 | semidirect |
| 79. C251 | #1666 | semidirect |
| 84. C8×Q8 | D251 | semidirect |
| 126. Q8 | #16860799 | semidirect |
| 142. C8 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632060 | 2 |
| #30631972 | 2 |
| #30631887 | 2 |
| #30631438 | 2 |
| #30631434 | 2 |
| #30631430 | 2 |
| C8×Q8×C251 | 2 |
| #1666 | 251 |