Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
412 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 3. C2×#22548625 | C2 | semidirect |
| 4. #30631441 | C2 | semidirect |
| 12. C22⋊(C251⋊C8) | C4 | semidirect |
| 16. C22⋊C8×C251 | C4 | semidirect |
| 24. C2×C251⋊C8 | C2×C4 | semidirect |
| 37. C2×C8×C251 | C2×C4 | semidirect |
| 66. C22×C251 | #97 | semidirect |
| 83. C251 | #1749 | semidirect |
| 99. C22⋊C8 | Dic251 | semidirect |
| 118. C2×C8 | C2×Dic251 | semidirect |
| 150. C22 | #22548625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic251 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×#22548625 | 2 |
| #30631441 | 2 |
| C2×C22⋊C8×C251 | 2 |
| #1749 | 251 |