Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30632416 | C2 | semidirect |
| 4. #30631432 | C2 | semidirect |
| 5. Q8⋊(C251⋊C8) | C2 | semidirect |
| 6. #30631417 | C2 | semidirect |
| 60. Q8×C251 | SD16 | semidirect |
| 90. C251 | #1626 | semidirect |
| 146. Q8 | #16860798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632416 | 2 |
| #30632033 | 2 |
| #30631884 | 2 |
| #30631432 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| #30631417 | 2 |
| #460×C251 | 2 |
| #1626 | 251 |