Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×M16×D251 | C2 | semidirect |
| 3. C2×#22548691 | C2 | semidirect |
| 4. #30631942 | C2 | semidirect |
| 5. #30631930 | C2 | semidirect |
| 6. #30631925 | C2 | semidirect |
| 7. #30631913 | C2 | semidirect |
| 8. #30631729 | C2 | semidirect |
| 9. #30631696 | C2 | semidirect |
| 10. #30631688 | C2 | semidirect |
| 11. C2×#137×C251 | C2 | semidirect |
| 33. #22548649 | C22 | semidirect |
| 34. #22548647 | C22 | semidirect |
| 35. #22548639 | C22 | semidirect |
| 36. #22548639 | C22 | semidirect |
| 37. #22548639 | C22 | semidirect |
| 38. #22548636 | C22 | semidirect |
| 42. C2×Q16×C251 | C22 | semidirect |
| 43. C2×SD16×C251 | C22 | semidirect |
| 90. M16×C251 | D4 | semidirect |
| 145. C2×D251 | #137 | semidirect |
| 163. C251 | #3056 | semidirect |
| 165. C2×#137 | D251 | semidirect |
| 180. C2×Q16 | C2×D251 | semidirect |
| 181. C2×SD16 | C2×D251 | semidirect |
| 236. M16 | C22⋊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 |
| #30632194 | 2 |
| C2×#22548691 | 2 |
| #30631942 | 2 |
| #30631930 | 2 |
| #30631925 | 2 |
| #30631913 | 2 |
| #30631729 | 2 |
| #30631696 | 2 |
| #30631688 | 2 |
| C2×#137×C251 | 2 |
| #3056 | 251 |