Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 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. #30632063 | C2 | semidirect |
| 2. #30631882 | C2 | semidirect |
| 3. #30631431 | C2 | semidirect |
| 4. D4⋊(C251⋊C8) | C2 | semidirect |
| 5. D42×C251 | C2 | semidirect |
| 8. #22548712 | C22 | semidirect |
| 9. C4⋊(C251⋊C8) | C22 | semidirect |
| 11. C4×C251⋊C8 | C22 | semidirect |
| 50. D4×C251 | D8 | semidirect |
| 74. C251 | #1619 | semidirect |
| 76. D42 | D251 | semidirect |
| 123. D4 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632063 | 2 |
| #30631882 | 2 |
| #30631431 | 2 |
| D4⋊(C251⋊C8) | 2 |
| D42×C251 | 2 |
| #1619 | 251 |