Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. #30631448 | C2 | semidirect |
| 5. #30631447 | C2 | semidirect |
| 6. #30631446 | C2 | semidirect |
| 7. #339×C251 | C2 | semidirect |
| 12. M16×D251 | C4 | semidirect |
| 15. #22548673 | C4 | semidirect |
| 18. #22548672 | C4 | semidirect |
| 21. C4⋊C4×D251 | C4 | semidirect |
| 42. #16860794 | C2×C4 | semidirect |
| 55. C4×Dic251 | C2×C4 | semidirect |
| 59. M16×C251 | C2×C4 | semidirect |
| 65. C42×C251 | C2×C4 | semidirect |
| 125. C251 | #1733 | semidirect |
| 133. #339 | D251 | semidirect |
| 173. M16 | C4×D251 | semidirect |
| 191. C42 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D251 | 2 |
| C2×#22548672 | 2 |
| #117×D251 | 2 |
| #30631448 | 2 |
| #30631447 | 2 |
| #30631446 | 2 |
| #339×C251 | 2 |
| #1733 | 251 |