Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
168 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 168 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. #30631818 | C2 | semidirect |
| 3. #30631438 | C2 | semidirect |
| 4. Q8⋊(C251⋊C8) | C2 | semidirect |
| 6. #30631409 | C2 | semidirect |
| 45. C251⋊C8 | SD16 | semidirect |
| 77. C251 | #1582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631818 | 2 |
| D4×C251⋊C8 | 2 |
| #30631438 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| D4⋊(C251⋊C8) | 2 |
| #30631409 | 2 |
| C4×SD16×C251 | 2 |
| #1582 | 251 |