Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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×#22548640 | C2 | semidirect |
| 4. C2×#22548638 | C2 | semidirect |
| 6. #30631449 | C2 | semidirect |
| 7. #340×C251 | C2 | semidirect |
| 13. #22548695 | C4 | semidirect |
| 32. C2×Dic502 | C2×C4 | semidirect |
| 61. C4⋊C4×C251 | C2×C4 | semidirect |
| 116. C2×D251 | #103 | semidirect |
| 134. C251 | #1872 | semidirect |
| 142. #340 | D251 | semidirect |
| 195. C4⋊C4 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548695 | 2 |
| C2×C4⋊C4×D251 | 2 |
| C2×#22548640 | 2 |
| C2×#22548638 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| #30631449 | 2 |
| #340×C251 | 2 |
| #1872 | 251 |