Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #30632033 | C2 | semidirect |
| 2. #30631967 | C2 | semidirect |
| 3. #30631892 | C2 | semidirect |
| 4. #30631431 | C2 | semidirect |
| 5. D4⋊(C251⋊C8) | C2 | semidirect |
| 6. D4⋊(C251⋊C8) | C2 | semidirect |
| 9. #22548715 | C22 | semidirect |
| 11. C4⋊(C251⋊C8) | C22 | semidirect |
| 12. C4⋊(C251⋊C8) | C22 | semidirect |
| 16. C4×C251⋊C8 | C22 | semidirect |
| 74. D4×C251 | SD16 | semidirect |
| 109. C251 | #1639 | semidirect |
| 180. D4 | #16860798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632033 | 2 |
| #30631967 | 2 |
| #30631892 | 2 |
| #30631431 | 2 |
| D4⋊(C251⋊C8) | 2 |
| D42×C251 | 2 |
| #1639 | 251 |